The document summarizes a student design project to reduce stress and twist in a swept forward aircraft wing. The students analyzed straight and swept wing models to compare displacement and stress. They used MATLAB to calculate spar locations that increased torsional rigidity in a hollow wing. Models with two or three spars were then analyzed in ANSYS. A 27 Newton lifting force was applied based on lift coefficient calculations. Tables compare results of different spar arrangements and thicknesses, identifying a three-spar design with 0.025, 0.01, and 0.01 cm thicknesses as providing the least twist and stress. Increasing the front spar thickness further reduced twist but increased stress due to added weight and bending moment.
The document describes an experiment to determine the Young's modulus of elasticity of mild steel, brass, and aluminum using a beam deflection method. The experiment involves applying various loads to beams made of each material and measuring the deflection with a dial gauge. Load-deflection graphs are plotted for each material, and the slope of the graphs is used to calculate the Young's modulus. The experiment found values of 1551 N/mm^2 for mild steel, 3675 N/mm^2 for brass, and 4963 N/mm^2 for aluminum. Precautions taken included carefully handling the dial gauge and ensuring accurate load placement and gauge positioning.
FEM_Modeling_Project_Evaluation of a Steel Pulley and Shaft DesignMehmet Bariskan
The document summarizes a finite element analysis (FEA) project evaluating the design of a steel pulley and shaft system. The initial FEA model found unrealistic stress concentrations and displacements due to invalid boundary conditions. The boundary conditions were customized and additional analyses were run with fillet radii of 1-5 mm added to reduce stress. Increasing the shaft diameter from 25mm to 30mm further reduced stress. The maximum stress was plotted against degrees of freedom for each model, with the 5mm fillet radius and 30mm shaft diameter model exhibiting the lowest stress of around 75MPa.
1. The document describes an experiment to determine the reactions at supports of a continuous beam subjected to point loads and uniformly distributed loads. Reactions are measured using load cells and compared to theoretical calculations.
2. For a beam with a point load, measured reactions were within 12% of calculations. For a beam with uniform loading, measured reactions matched calculations within 4% except at one support where they matched exactly.
3. Differences between measured and calculated reactions are likely due to imperfections in the old laboratory apparatus and effects of airflow on measurements. The experiment successfully validated the theoretical reactions within an acceptable margin of error.
Deflection of simply supported beam and cantileveryashdeep nimje
This document describes experiments to measure the deflection of simply supported beams and cantilever beams under different loading conditions. For simply supported beams, deflection increases linearly with applied load and decreases with beam length. Deflection measurements match theoretical calculations. For cantilever beams, deflection increases linearly with both applied load and distance from the fixed end. The experiments demonstrate linear relationships between load/position and deflection as predicted by theory.
When a solid body deforms due to external loads or temperature changes, it experiences strain. Normal strain refers to the elongation or contraction of a line segment per unit length. Shear strain is the change in angle between two originally perpendicular line segments. For most engineering applications, only small deformations and strains are considered in the analysis.
This document summarizes a Finite Element Analysis (FEA) project evaluating the stress on a pulley design. The initial simulation found unexpected high stress, so boundary conditions were adjusted by adding restraints on the pulley bores. However, a re-entrant edge at the shaft-bore connection caused stress singularities. Adding a 1mm fillet removed this issue, and subsequent local mesh refinement showed stress values converging, validating the design.
This document summarizes the mechanical properties of materials through stress-strain diagrams. It discusses the differences between stress-strain diagrams for ductile versus brittle materials. For ductile materials, the diagram shows elastic behavior, yielding, strain hardening, necking, and true stress-strain. Brittle materials exhibit no yielding and rupture occurs at a much smaller strain. The document also discusses Hooke's law, Poisson's ratio, axial loading of materials, and provides examples of calculating deformation based on applied loads and material properties.
This document discusses unsymmetric bending, where the resultant internal moment does not act about one of the principal axes of a cross section. It explains that the moment should first be resolved into components directed along the principal axes. The flexure formula can then be used to determine the normal stress caused by each moment component. Finally, the resultant normal stress at each point can be determined using the principle of superposition. It also provides an equation to determine the orientation of the neutral axis for an unsymmetrically loaded cross section.
The document describes an experiment to determine the Young's modulus of elasticity of mild steel, brass, and aluminum using a beam deflection method. The experiment involves applying various loads to beams made of each material and measuring the deflection with a dial gauge. Load-deflection graphs are plotted for each material, and the slope of the graphs is used to calculate the Young's modulus. The experiment found values of 1551 N/mm^2 for mild steel, 3675 N/mm^2 for brass, and 4963 N/mm^2 for aluminum. Precautions taken included carefully handling the dial gauge and ensuring accurate load placement and gauge positioning.
FEM_Modeling_Project_Evaluation of a Steel Pulley and Shaft DesignMehmet Bariskan
The document summarizes a finite element analysis (FEA) project evaluating the design of a steel pulley and shaft system. The initial FEA model found unrealistic stress concentrations and displacements due to invalid boundary conditions. The boundary conditions were customized and additional analyses were run with fillet radii of 1-5 mm added to reduce stress. Increasing the shaft diameter from 25mm to 30mm further reduced stress. The maximum stress was plotted against degrees of freedom for each model, with the 5mm fillet radius and 30mm shaft diameter model exhibiting the lowest stress of around 75MPa.
1. The document describes an experiment to determine the reactions at supports of a continuous beam subjected to point loads and uniformly distributed loads. Reactions are measured using load cells and compared to theoretical calculations.
2. For a beam with a point load, measured reactions were within 12% of calculations. For a beam with uniform loading, measured reactions matched calculations within 4% except at one support where they matched exactly.
3. Differences between measured and calculated reactions are likely due to imperfections in the old laboratory apparatus and effects of airflow on measurements. The experiment successfully validated the theoretical reactions within an acceptable margin of error.
Deflection of simply supported beam and cantileveryashdeep nimje
This document describes experiments to measure the deflection of simply supported beams and cantilever beams under different loading conditions. For simply supported beams, deflection increases linearly with applied load and decreases with beam length. Deflection measurements match theoretical calculations. For cantilever beams, deflection increases linearly with both applied load and distance from the fixed end. The experiments demonstrate linear relationships between load/position and deflection as predicted by theory.
When a solid body deforms due to external loads or temperature changes, it experiences strain. Normal strain refers to the elongation or contraction of a line segment per unit length. Shear strain is the change in angle between two originally perpendicular line segments. For most engineering applications, only small deformations and strains are considered in the analysis.
This document summarizes a Finite Element Analysis (FEA) project evaluating the stress on a pulley design. The initial simulation found unexpected high stress, so boundary conditions were adjusted by adding restraints on the pulley bores. However, a re-entrant edge at the shaft-bore connection caused stress singularities. Adding a 1mm fillet removed this issue, and subsequent local mesh refinement showed stress values converging, validating the design.
This document summarizes the mechanical properties of materials through stress-strain diagrams. It discusses the differences between stress-strain diagrams for ductile versus brittle materials. For ductile materials, the diagram shows elastic behavior, yielding, strain hardening, necking, and true stress-strain. Brittle materials exhibit no yielding and rupture occurs at a much smaller strain. The document also discusses Hooke's law, Poisson's ratio, axial loading of materials, and provides examples of calculating deformation based on applied loads and material properties.
This document discusses unsymmetric bending, where the resultant internal moment does not act about one of the principal axes of a cross section. It explains that the moment should first be resolved into components directed along the principal axes. The flexure formula can then be used to determine the normal stress caused by each moment component. Finally, the resultant normal stress at each point can be determined using the principle of superposition. It also provides an equation to determine the orientation of the neutral axis for an unsymmetrically loaded cross section.
1. The document discusses bending deformation that occurs in a straight beam made of a homogeneous material when subjected to bending. It describes how the beam's cross-section and longitudinal lines distort under an applied bending moment.
2. It notes that the bottom of the beam stretches and the top compresses, with a neutral surface in between that does not change length. Key assumptions are presented about how the stress deforms the material.
3. Equations are developed relating normal strain and stress to the beam's geometry and applied bending moment, with stress varying linearly from compression at the top to tension at the bottom. The location of the neutral axis is also described.
The aim of the experiment is to find the flexural rigidity (EI) of a beam and compare it to the theoretical value. A beam with overhangs is loaded at the free ends and the central deflection is measured for different loads. The flexural rigidity is calculated using the measured deflection and load values and beam properties. This calculated EI is then compared to the theoretical EI calculated using the beam's cross-section dimensions and modulus of elasticity. Observing the beam's deflection under various loads allows determining its flexural rigidity and verifying beam theory calculations.
This document discusses shear flow in built-up members, which are structural members constructed from composite parts joined together. It provides a formula to calculate the shear flow along the junction between composite parts based on the internal shear force, moment of inertia, and moment of a segment's area about the neutral axis. Examples are given to demonstrate calculating shear flow at specific points that must be resisted by fasteners joining the composite parts.
Composites are made of two main components: fibers and a matrix. Fibers carry load and can be made of materials like glass, carbon, and Kevlar. Fibers come in various forms like strands, woven meshes, and chopped fibers. The matrix is a fluid that hardens and holds the fibers in place. It can be made of materials like plastic. Examples of composites include carbon fiber and plastic skis, Kevlar and fiberglass boats, and concrete reinforced with steel. The document then discusses stresses in beams including bending stresses, maximum bending stress, and shear stress.
The document discusses various methods for analyzing beam deflection and deformation under loading, including:
1) Deriving the differential equation for the elastic curve of a beam and applying boundary conditions to determine the curve and maximum deflection.
2) Using the method of superposition to analyze beams subjected to multiple loadings by combining the effects of individual loads.
3) Applying moment-area theorems which relate the bending moment diagram to slope and deflection, allowing deflection calculations for beams with various support conditions.
This document provides an introduction to strength of materials, including concepts of stress, strain, Hooke's law, stress-strain relationships, elastic constants, and factors of safety. It defines key terms like stress, strain, elastic limit, modulus of elasticity, and ductile and brittle material behavior. Examples of stress and strain calculations are provided for basic structural elements like rods, bars, and composite structures. The document also covers compound bars, principle of superposition, and effects of temperature changes.
1. The document describes a problem involving the elongation of a tapered bar made of plastic that has a hole drilled through part of its length and is under compressive loads at its ends.
2. It provides the dimensions, material properties, and loads and asks for the maximum diameter of the hole if the shortening of the bar is limited to 8 mm.
3. The solution sets up an equation for the shortening of the bar in terms of the hole diameter and substitutes the given values to solve for the maximum hole diameter of 23.9 mm.
Solution of Chapter- 05 - stresses in beam - Strength of Materials by SingerAshiqur Rahman Ziad
This document discusses stresses in beams, including flexural and shearing stresses. It provides formulas for calculating flexural stress based on the beam's moment of inertia, bending moment, and distance from the neutral axis. Several example problems are worked through applying these formulas. The document also discusses using economic beam sections that optimize the use of material by placing more area on the outer fibers where stresses are highest.
The document discusses allowable axial compressive loads on structural members. It describes key factors that influence a member's capacity including length, cross-sectional area, material properties, and end fixity. The column buckling formula developed by Euler is presented, as well as the American Institute of Steel Construction (AISC) approach for analyzing and designing columns based on the slenderness ratio.
1) The document reports on a beam analysis simulation where beams were subjected to uniform and non-uniform loads.
2) Maximum displacements, stresses, and bending moments were reported from the simulation for different mesh element sizes.
3) Beam differential equations were derived for uniform and non-uniform loads and solved to find theoretical deflections.
4) The theoretical deflections did not match the simulation results, likely due to additional loading conditions and deflection absorption in the simulation that were not accounted for in the simplified theoretical model.
Shear Force And Bending Moment Diagram For FramesAmr Hamed
This document discusses analyzing shear and moment diagrams for frames. It provides procedures for determining reactions, axial forces, shear forces, and moments at member ends. Examples are given of drawing shear and moment diagrams for simple frames with different joint conditions, including pin and roller supports. Diagrams for a three-pin frame example are shown.
Analysis of Multi-storey Building Frames Subjected to Gravity and Seismic Loa...Pralhad Kore
This document summarizes the results of analyzing 3-bay, 5-bay, and 7-bay 9-story reinforced concrete frames with varying geometric properties under gravity and seismic loads. The response of frames was studied when incorporating idealized T-beams between points of contraflexure in beams and providing haunches of varying widths at beam-column joints. Results found that axial forces in columns increased linearly from top to bottom, while bending moments decreased with larger beam-column stiffness ratios. Lateral displacements under seismic loads were reduced by incorporating T-beams and haunches, demonstrating their beneficial effects on structural response.
Approximate analysis methods make simplifying assumptions to determine preliminary member forces and dimensions for indeterminate structures. Case 1 assumes diagonals cannot carry compression and shares shear between diagonals. Case 2 allows compression in diagonals. Portal and cantilever methods analyze frames by dividing into substructures at assumed hinge locations, solving each sequentially from top to bottom.
The document discusses various mechanical properties of materials including:
1) Ultimate strength is the maximum stress a material can withstand before fracturing.
2) Yield strength is the maximum stress before permanent deformation occurs.
3) Modulus of elasticity is the ratio of stress to strain in the linear region.
It also discusses allowable stress which is determined using a factor of safety applied to the yield or ultimate strength to ensure stresses do not exceed yield strength and accounts for flaws. An example calculates the minimum cable diameter required to safely support a 200lb load from 300ft.
This document discusses beam design criteria and deflection behavior of beams. It covers two key criteria for beam design:
1) Strength criterion - the beam cross section must be strong enough to resist bending moments and shear forces.
2) Stiffness criterion - the maximum deflection of the beam cannot exceed a limit and the beam must be stiff enough to resist deflections from loading.
It then defines deflection, slope, elastic curve, and flexural rigidity. It presents the differential equation that relates bending moment, slope, and deflection. Methods for calculating slope and deflection including double integration, Macaulay's method, and others are also summarized.
The cable produces a total pull of 220 kN at the top of the anchorage. Let's break this problem down step-by-step:
1) Resolve the 220 kN force into horizontal (RAH) and vertical (RAV) components:
RAH = 220 cos 30° = 191 kN
RAV = 220 sin 30° = -196 kN (note the negative sign indicates downward direction)
2) The horizontal and vertical equilibrium equations are satisfied:
ΣH = RAH - 0 = 0
ΣV = RAV - (-196) = 0
Therefore, the support reactions are:
RAH = 191 kN
RAV = -196 kN
This document discusses bending moments and shear forces in beams. It defines different types of beams such as simply supported beams, cantilever beams, and beams with overhangs. It also defines types of loads like concentrated loads, distributed loads, and couples. It explains how to calculate the shear force and bending moment at any cross-section of a beam and discusses relationships between loads, shear forces and bending moments. It provides examples of drawing shear force and bending moment diagrams. Finally, it discusses bending stresses in beams and bending of beams made of two materials.
This book is intended to cover the basic Strength of Materials of the first
two years of an engineering degree or diploma course ; it does not attempt
to deal with the more specialized topics which usually comprise the final
year of such courses.
The work has been confined to the mathematical aspect of the subject
and no descriptive matter relating to design or materials testing has been
included.
06-Strength of Double Angle Welded Tension Members (Steel Structural Design &...Hossam Shafiq II
1. The document discusses the strength of double angle welded tension members. It describes three failure modes: yielding of the gross area, fracture of the effective area, and block shear rupture in the angle.
2. Formulas are provided to calculate the nominal resistance (Rn) for each failure mode based on the yield strength, ultimate tensile strength, and dimensions of the angles.
3. An example problem is worked through to determine the governing strength of a specific welded double angle configuration based on the provided dimensions and material properties. The yielding of the gross area controls with a nominal resistance of 459 kN.
MMAE545-Final Report-Analysis of Aircraft WingLI HE
This report summarizes an analysis of an aircraft wing conducted by three members. The analysis included CAD modeling of the wing geometry, mesh generation, and static and dynamic simulations. For the static analysis, three loading conditions were analyzed: steady flight, overloading, and rolling. Peak stresses were found to be below material limits for all conditions. Natural frequencies and mode shapes were determined, and impact simulations were run at different locations and masses to study structural response. Recommendations for future weight reduction include adding holes to ribs and using thinner carbon fiber.
This document summarizes a student project to design a trebuchet catapult made of MDF that could launch a ping pong ball 12 meters. The student analyzed the design using statics, kinematics and MATLAB. Parameters like arm lengths and counterweight size were varied in the MATLAB analysis to determine optimal dimensions. An Arduino controlled servo was used as the release mechanism. The final design was tested and improvements were made based on weaknesses found during testing.
1. The document discusses bending deformation that occurs in a straight beam made of a homogeneous material when subjected to bending. It describes how the beam's cross-section and longitudinal lines distort under an applied bending moment.
2. It notes that the bottom of the beam stretches and the top compresses, with a neutral surface in between that does not change length. Key assumptions are presented about how the stress deforms the material.
3. Equations are developed relating normal strain and stress to the beam's geometry and applied bending moment, with stress varying linearly from compression at the top to tension at the bottom. The location of the neutral axis is also described.
The aim of the experiment is to find the flexural rigidity (EI) of a beam and compare it to the theoretical value. A beam with overhangs is loaded at the free ends and the central deflection is measured for different loads. The flexural rigidity is calculated using the measured deflection and load values and beam properties. This calculated EI is then compared to the theoretical EI calculated using the beam's cross-section dimensions and modulus of elasticity. Observing the beam's deflection under various loads allows determining its flexural rigidity and verifying beam theory calculations.
This document discusses shear flow in built-up members, which are structural members constructed from composite parts joined together. It provides a formula to calculate the shear flow along the junction between composite parts based on the internal shear force, moment of inertia, and moment of a segment's area about the neutral axis. Examples are given to demonstrate calculating shear flow at specific points that must be resisted by fasteners joining the composite parts.
Composites are made of two main components: fibers and a matrix. Fibers carry load and can be made of materials like glass, carbon, and Kevlar. Fibers come in various forms like strands, woven meshes, and chopped fibers. The matrix is a fluid that hardens and holds the fibers in place. It can be made of materials like plastic. Examples of composites include carbon fiber and plastic skis, Kevlar and fiberglass boats, and concrete reinforced with steel. The document then discusses stresses in beams including bending stresses, maximum bending stress, and shear stress.
The document discusses various methods for analyzing beam deflection and deformation under loading, including:
1) Deriving the differential equation for the elastic curve of a beam and applying boundary conditions to determine the curve and maximum deflection.
2) Using the method of superposition to analyze beams subjected to multiple loadings by combining the effects of individual loads.
3) Applying moment-area theorems which relate the bending moment diagram to slope and deflection, allowing deflection calculations for beams with various support conditions.
This document provides an introduction to strength of materials, including concepts of stress, strain, Hooke's law, stress-strain relationships, elastic constants, and factors of safety. It defines key terms like stress, strain, elastic limit, modulus of elasticity, and ductile and brittle material behavior. Examples of stress and strain calculations are provided for basic structural elements like rods, bars, and composite structures. The document also covers compound bars, principle of superposition, and effects of temperature changes.
1. The document describes a problem involving the elongation of a tapered bar made of plastic that has a hole drilled through part of its length and is under compressive loads at its ends.
2. It provides the dimensions, material properties, and loads and asks for the maximum diameter of the hole if the shortening of the bar is limited to 8 mm.
3. The solution sets up an equation for the shortening of the bar in terms of the hole diameter and substitutes the given values to solve for the maximum hole diameter of 23.9 mm.
Solution of Chapter- 05 - stresses in beam - Strength of Materials by SingerAshiqur Rahman Ziad
This document discusses stresses in beams, including flexural and shearing stresses. It provides formulas for calculating flexural stress based on the beam's moment of inertia, bending moment, and distance from the neutral axis. Several example problems are worked through applying these formulas. The document also discusses using economic beam sections that optimize the use of material by placing more area on the outer fibers where stresses are highest.
The document discusses allowable axial compressive loads on structural members. It describes key factors that influence a member's capacity including length, cross-sectional area, material properties, and end fixity. The column buckling formula developed by Euler is presented, as well as the American Institute of Steel Construction (AISC) approach for analyzing and designing columns based on the slenderness ratio.
1) The document reports on a beam analysis simulation where beams were subjected to uniform and non-uniform loads.
2) Maximum displacements, stresses, and bending moments were reported from the simulation for different mesh element sizes.
3) Beam differential equations were derived for uniform and non-uniform loads and solved to find theoretical deflections.
4) The theoretical deflections did not match the simulation results, likely due to additional loading conditions and deflection absorption in the simulation that were not accounted for in the simplified theoretical model.
Shear Force And Bending Moment Diagram For FramesAmr Hamed
This document discusses analyzing shear and moment diagrams for frames. It provides procedures for determining reactions, axial forces, shear forces, and moments at member ends. Examples are given of drawing shear and moment diagrams for simple frames with different joint conditions, including pin and roller supports. Diagrams for a three-pin frame example are shown.
Analysis of Multi-storey Building Frames Subjected to Gravity and Seismic Loa...Pralhad Kore
This document summarizes the results of analyzing 3-bay, 5-bay, and 7-bay 9-story reinforced concrete frames with varying geometric properties under gravity and seismic loads. The response of frames was studied when incorporating idealized T-beams between points of contraflexure in beams and providing haunches of varying widths at beam-column joints. Results found that axial forces in columns increased linearly from top to bottom, while bending moments decreased with larger beam-column stiffness ratios. Lateral displacements under seismic loads were reduced by incorporating T-beams and haunches, demonstrating their beneficial effects on structural response.
Approximate analysis methods make simplifying assumptions to determine preliminary member forces and dimensions for indeterminate structures. Case 1 assumes diagonals cannot carry compression and shares shear between diagonals. Case 2 allows compression in diagonals. Portal and cantilever methods analyze frames by dividing into substructures at assumed hinge locations, solving each sequentially from top to bottom.
The document discusses various mechanical properties of materials including:
1) Ultimate strength is the maximum stress a material can withstand before fracturing.
2) Yield strength is the maximum stress before permanent deformation occurs.
3) Modulus of elasticity is the ratio of stress to strain in the linear region.
It also discusses allowable stress which is determined using a factor of safety applied to the yield or ultimate strength to ensure stresses do not exceed yield strength and accounts for flaws. An example calculates the minimum cable diameter required to safely support a 200lb load from 300ft.
This document discusses beam design criteria and deflection behavior of beams. It covers two key criteria for beam design:
1) Strength criterion - the beam cross section must be strong enough to resist bending moments and shear forces.
2) Stiffness criterion - the maximum deflection of the beam cannot exceed a limit and the beam must be stiff enough to resist deflections from loading.
It then defines deflection, slope, elastic curve, and flexural rigidity. It presents the differential equation that relates bending moment, slope, and deflection. Methods for calculating slope and deflection including double integration, Macaulay's method, and others are also summarized.
The cable produces a total pull of 220 kN at the top of the anchorage. Let's break this problem down step-by-step:
1) Resolve the 220 kN force into horizontal (RAH) and vertical (RAV) components:
RAH = 220 cos 30° = 191 kN
RAV = 220 sin 30° = -196 kN (note the negative sign indicates downward direction)
2) The horizontal and vertical equilibrium equations are satisfied:
ΣH = RAH - 0 = 0
ΣV = RAV - (-196) = 0
Therefore, the support reactions are:
RAH = 191 kN
RAV = -196 kN
This document discusses bending moments and shear forces in beams. It defines different types of beams such as simply supported beams, cantilever beams, and beams with overhangs. It also defines types of loads like concentrated loads, distributed loads, and couples. It explains how to calculate the shear force and bending moment at any cross-section of a beam and discusses relationships between loads, shear forces and bending moments. It provides examples of drawing shear force and bending moment diagrams. Finally, it discusses bending stresses in beams and bending of beams made of two materials.
This book is intended to cover the basic Strength of Materials of the first
two years of an engineering degree or diploma course ; it does not attempt
to deal with the more specialized topics which usually comprise the final
year of such courses.
The work has been confined to the mathematical aspect of the subject
and no descriptive matter relating to design or materials testing has been
included.
06-Strength of Double Angle Welded Tension Members (Steel Structural Design &...Hossam Shafiq II
1. The document discusses the strength of double angle welded tension members. It describes three failure modes: yielding of the gross area, fracture of the effective area, and block shear rupture in the angle.
2. Formulas are provided to calculate the nominal resistance (Rn) for each failure mode based on the yield strength, ultimate tensile strength, and dimensions of the angles.
3. An example problem is worked through to determine the governing strength of a specific welded double angle configuration based on the provided dimensions and material properties. The yielding of the gross area controls with a nominal resistance of 459 kN.
MMAE545-Final Report-Analysis of Aircraft WingLI HE
This report summarizes an analysis of an aircraft wing conducted by three members. The analysis included CAD modeling of the wing geometry, mesh generation, and static and dynamic simulations. For the static analysis, three loading conditions were analyzed: steady flight, overloading, and rolling. Peak stresses were found to be below material limits for all conditions. Natural frequencies and mode shapes were determined, and impact simulations were run at different locations and masses to study structural response. Recommendations for future weight reduction include adding holes to ribs and using thinner carbon fiber.
This document summarizes a student project to design a trebuchet catapult made of MDF that could launch a ping pong ball 12 meters. The student analyzed the design using statics, kinematics and MATLAB. Parameters like arm lengths and counterweight size were varied in the MATLAB analysis to determine optimal dimensions. An Arduino controlled servo was used as the release mechanism. The final design was tested and improvements were made based on weaknesses found during testing.
The finite element analysis determined the suitability of a titanium panel to replace the floor of a rescue helicopter. Three mission scenarios were modeled: 1) with a 100kg winch attached and the panel built-in, 2) with the winch attached and the panel simply supported, and 3) with distributed 10kg grain sacks and the panel built-in. Finite element models were generated and found to accurately predict stress and deflection, matching analytical calculations. The models determined that scenario 1 and 2 posed no yield risk, and the helicopter could safely carry at least 250 grain sacks in scenario 3.
Designed a torque arm, with Multi Point Constraints applied to the center of the arm. The FEA software used for this purpose was ABAQUS. The analysis was performed two major element types: Triangular Elements and Quadrilateral Elements, with relatively equal number of nodes in each case and a convergence study was conducted. The aim of the project was to obtain the optimal design parameters of the torque arm by optimization (minimize weight).
Final Project_ Design and FEM Analysis of Scissor JackMehmet Bariskan
The document describes the design and finite element analysis of a scissor jack. It includes an overview of scissor jack components and operation, as well as calculations of forces and stresses on members. A series of mesh refinement studies were performed on the carrier member, lifting arms, and shaft screw to determine maximum stresses and displacements under expected loading conditions.
2016 optimisation a rear wing endplate in a rotating domainHashan Mendis
This document discusses the optimization of end plates on a rear wing for a Formula SAE race car through computational fluid dynamics simulations. It describes setting up models of the initial and modified end plate designs in both straight line and rotating flow domains. The simulations found that while the modified end plate design produced similar downforce and drag as the initial design in a straight line, it reduced side force by 20% in the rotating domain, indicating more efficient performance under yaw conditions. Mesh studies were conducted to ensure grid independence. The modified end plate design optimized the end plate shape to better manage the flow vortices and pressure distribution during cornering.
The document describes the design, construction, and testing of a trebuchet built by a student for a class project. The trebuchet was required to launch a water-filled ping pong ball 12 meters, which it successfully accomplished after several design iterations. The student used analysis and calculations to optimize the design in areas such as forces on components, stress levels, and launch angles. Through rigorous testing and redesign, the student was able to complete the project of building a functional trebuchet meeting the specified performance goals.
ME 5720 Fall 2015 - Wind Turbine Project_FINALOmar Latifi
This document summarizes a project analyzing the design of a composite laminate for the spar of a wind turbine blade. A MATLAB code was developed to calculate stresses and determine if a proposed 7-ply hybrid glass fiber/carbon fiber laminate [0/45/0/45/0/45/0] would fail when subjected to expected wind loads. The code calculated lamina properties, stiffness matrices, strains and stresses for each ply. The Tsai-Hill failure criteria was applied and indicated the laminate would not fail. Therefore, the hybrid laminate was determined to be a viable solution for withstanding the loads on the spar.
Final Report Turbulant Flat Plate AnsysSultan Islam
- The document describes a computational fluid dynamics (CFD) simulation of turbulent flow over a flat plate using ANSYS CFX.
- The simulation aims to validate results against experimental data from NASA and analyze sensitivity of skin friction coefficient and velocity profiles.
- The flat plate geometry, meshing approach, and boundary conditions are described based on the NASA and Caelus experiments.
- Results for velocity profiles and skin friction coefficients along the plate are presented and validated against experimental trends.
- Grid convergence and sensitivity to turbulence models are analyzed, with the SST and k-epsilon models showing similar results.
This document presents a computational analysis of the structural components and behavior of flexible aircraft. It describes a MATLAB code used to determine natural frequencies and loads of a cantilever wing with stores in different spanwise positions. The code calculates natural frequencies from mass and stiffness matrices. Basis functions are used to represent bending and torsional modes. Validation shows computed torsion frequencies match experimental data, while bending frequencies have some offset. Parameters like store mass and position are investigated and found to affect natural frequencies.
Finite Element Model Establishment and Strength Analysis of Crane BoomSuresh Ramarao
1) The document establishes a finite element model of a crane boom in Ansys software by first building a 3D model in SolidWorks and then importing it into Ansys to define properties and mesh.
2) A strength analysis is performed on the boom model in Ansys by applying constraints and loads corresponding to working conditions. The maximum stress is found to be 252 MPa in the boom head.
3) Results from the Ansys analysis are compared to theoretical calculations, finding an error of around 3.3% for stress in a dangerous section, validating the accuracy of the finite element model.
The document summarizes a finite element analysis of a torque arm performed in Abaqus to optimize the design. It includes:
1) A preliminary analysis using mechanics of materials approximations to estimate stress and displacement.
2) An analysis of different element types to determine appropriate meshing.
3) A convergence study to determine optimal mesh size.
4) A parameter study that varies arm dimensions to minimize mass while meeting stress constraints.
The analysis aims to find the lightest torque arm design that keeps stresses below 240 MPa.
A finite element analysis was performed on a 6 bay plane truss structure using ABAQUS software to determine deflections and member forces under tension, shear, and bending loads. The results were used to calculate equivalent cross-sectional properties, assuming the truss behaved like a cantilever beam. Additional analysis was conducted using fully stressed design to minimize the structure's weight by resizing members to be fully stressed at their allowable limit of 100 MPa under at least one load case, while maintaining a minimum gauge of 0.1 cm^2. Iterative resizing reduced member areas and increased stresses until all members were fully stressed at their limits.
This document describes an experiment to determine the shear force and bending moment of a beam using an apparatus. It includes the objective, apparatus description, related theory, procedure, sample calculations and results in tables and graphs. The conclusions are that there is a linear relationship between load and shear force/bending moment, and experimental results match theoretical values closely. Applications of shear force and bending moment diagrams in structural design are also discussed.
This document outlines an experiment to measure strain on a cantilever beam using resistance strain gauges. It includes an introduction explaining strain measurement using strain gauges, objectives of learning how to use strain indicators and apply uncertainty analysis. The methodology section details the equipment used including a cantilever beam, strain gauges, weights and amplifier. The experimentation section provides steps to mount the beam, zero the amplifier, record strain measurements at different beam lengths and weight amounts. The results section shows tables of strain values measured. Finally, the conclusions note that strain increased with increasing beam length and load amount as expected.
This project modeled an Easton EC70 XC handlebar using beam, solid, and shell element models in ABAQUS to analyze stresses, strains, and deflections under common loading cases. A shell model with a swept mesh was found to be the most accurate and efficient. Various layup configurations were tested for carbon fiber, aluminum, and steel materials. The [0°/0°/+45°/-45°] carbon layup provided the best strength-to-weight ratio, withstanding over 300 lbf of end load or 2600 lbf-in of torque. While hand calculations validated model results, the true layup is unknown but assumed to be mostly 0° plies for bending strength with additional angles for
This document is a phase 2 report from a structural engineering project team analyzing a hotel structure. It recaps the assumptions made in phase 1 and presents the experimental results, which showed significant differences from the theoretical predictions. This was likely due to not accounting for eccentric loading and variances in how the top plate was attached. While the predictions were not highly accurate, removing bracing on the south side still satisfies safety codes and the client's needs.
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The document summarizes the analysis and design of various foundation types for a seven story building in Nablus city. It describes isolated footings, combined footings, wall footings, mat foundations, and pile foundations. Laboratory test results of soil samples are presented. Loads on each column are calculated. Dimensions, reinforcement details and settlement calculations are provided for each foundation type. Based on the analysis of material quantities, construction costs, and settlement calculations, isolated footings with combined, wall and elevator footings are recommended as the most economical foundation solution.
Solid_Modeling_Project_#2_ Reverse engineering of a connecting rod and docume...Mehmet Bariskan
This document summarizes a student's solid modeling project to create a computer-aided design (CAD) model of a connecting rod through reverse engineering. The student followed these steps: 1) Creating a freehand sketch of the connecting rod using measurements; 2) Developing a solid model in SolidWorks based on the sketch; 3) Creating technical drawings of the model; 4) Performing a finite element analysis to evaluate stresses and deformation under load. The analysis found the highest stresses occurred near where loads were applied. Though within safety factors, real connecting rods can still break due to unmodeled factors like fatigue not considered.
2. 2
Swept forward wing has significant aerodynamic advantages over straight wings when
Mach number approaching or exceeding 1. However, different from Straight wing which
experience only bending deformation, swept forward wing is easily affected by torsional
deformation which cause the wing to twist. The main focus of the project is to come out with a
design with reduced stress and twist for a swept forward wing with Gottingen 398 as the airfoil
shape by changing the internal structure of the wing. The airfoil coordinates are shown in
Appendix A. Throughout our study, we will use the property of balsa wood for material, which
will be shown in Table 2.
Part I – Comparison between straight and swept forward wing
The first step in designing the wing, is comparing the displacement difference between
straight wing and swept forward wing. In this part both of the wings are solid, and 1 newton
force is applied along the ¼ cord with the wing ends fixed. We will keep using 1 newton force
during the first part and when we analyze the wing section geometry to make sure the force is
constant and not affecting the result.
From the study we found displacement is very even along the wing section in the straight
wing and that the difference is very small compared to what we get from a swept forward wing.
The displacement plot of both wings will be shown in Figure 1. By adjusting the position of the
lifting force along the wing section on the straight wing, we are able to get analysis results with
angles of twist close to zero (shown in figure 2). This means that we have applied the lifting
force on the shear center. However, for the swept forward wing, the leading edge will always be
experiencing higher displacement than the trailing edge so we believe the shear center is outside
the wing and that twisting is so serious in a swept forward wing. From the stress analysis which
will be shown in figure 3, we also found that the stress is concentrated around the center part of
the wing section at the wing end, while for the swept forward wing the maximum stress will be
found around front part at the wing end.
Table 1: comparison of displacement
lift at 1/4 cord
leading(m) trailing(m) difference(m)
straight 6.99E-05 6.76E-05 2.27E-06
swept forward 8.71E-05 7.36E-05 1.35E-05
lift at 4.8cm from leading edge
straight 6.91E-05 6.89E-05 1.97E-07
Table 2: material properties
property of the material
Elastic Modulus: 3.71Gpa
Density: 0.13g/cm^3
3. 3
a)
b)
Figure 1: displacement plot :
a) the straight wing, 6.764e-5m at the trailing edge,6.9909e-5m at leading edge
b) the swept wing: 9.259039157e-5 m at trailing edge,8.041581446e-5 mat leading edge
4. 4
Figure 2: displacement of the straight wing when lifting force is applied along the 4.8cm edge from the leading edge:
6.9097e-5m at leading edge, 6.89e-5m at trailing edge
a)
b)
Figure 3: stress plot with lift along ¼ chord: a)straight wing,b)swept forward wing
5. 5
Part II -- Calculation
While hollowing, the first challenge was to determine how many spars we would use and
the location of the spars. We did some online research on how people calculated the shear center
of a multicell wing section to find any approximations in order to make the calculations easier1.
We noticed that the calculations for the shear flow on the spars were the largest and that the ribs
did not have that much effect on the deflection. We decided to focus on two or three spars
because we did not want to add more weight to the wing and it appeared that two to three spars
were typically used in previous designs.
To find the location of the spars we used MATLAB write a function code to calculate the
rigidity of the straight wing if we used two or three spars. The function code had the normalized
coordinates of the Gottingen 398 airfoil and was able to calculate new y coordinates if we
changed the spacing of each x coordinate by linear interpolation. Then the code calculated the
height of the cell walls that would be the height of the spars. After that, the code calculated the
cell areas and the top and bottom wall lengths. With these values the code created a matrix of the
linear equations of the equation theta = 1/(2*Aof cell)*(line integral of q/t ds) for each cell and at
the end of the matrix it would have the equation for torque T = 2*(sum of Aof each cell times
shear flow of each cell). The shear flow for each cell was solved and the end result had the
torsional stiffness of G*theta/T (called “Stiffness”) for the cross section. This torsional stiffness
was compared to the single cell, i.e. no spars case and gave us a ratio called “StiffScaled”. For
the two spar code, the largest increase in torsional rigidity(rigidity ratio) was 16% compared to
the single cell. The code shows the results of the locations of the spars that had over 16%
increase in torsional rigidity. For the three spar code, the largest increase in torsional rigidity was
20% and again our code shows the results of the locations of the sars that had over 20% increase
in torsional rigidity. The MATLAB codes can be referenced in Appendix B.
With the result we found in MATLAB, we made different SolidWorks models with two
or three spars and did a lot of trials in ANSYS, then decided to use the normalized locations of
0.1, 0.45 and 0.7 from the leading edge with normalized thicknesses of 0.025, 0.01, and 0.01 for
the spars. This combination of location and thicknesses had the lowest maximum principal stress
on the wing and fairly low angle of twist. At this point we realized we should do our ANSYS
simulation with a more realistic lift force, so we used 27 Newtons assuming that was the lift
force in the wing at 75 mph wind speed (33.5 m/s). From the plot of cl vs. angle of attack, shown
in graph 1, we found the cl to 0.8 at 10-degree angle attack.The calculation used the following
formula, assuming an air density of 1.225 kg/m3:
FLift = 0.5 ∗ 𝑐𝑐 ∗ 𝑐 ∗ 𝑐2
∗ ∫𝑐
𝑐𝑐
𝑐𝑐𝑐𝑐
FLift = (0.5)*0.8*(1.225 kg/m3)*[(75 mph)(0.447 m/s/m1ph)]2*[12cm * 40cm]= 27N
1
Website for multicell beams in torsion: http://www.aeromech.usyd.edu.au/structures/acs1-p83.html
6. 6
graph1:lift coefficient vs angle of attack for Gottingen 398 airfoil
Part III – Analysis ofthe Wing Section
To find out which wing section design gives us the least twist and maximum stress, we
will keep the lifting force constant as 1 Newton and the designs will have no rib adding in this
part of study. During the analysis, we need to keep in mind that twist is unavoidable for a swept
forward wing because its shear center is at the back of the wing and we will be trying our best to
move the shear center forward. From the result of the MatLab calculation, we have decided the
designs we want to look into. Then we change the thicknesses of the section walls, which are the
spars in the wing, and analyze to decide the best wing section geometry. The results and analysis
of the wing section geometry will be shown in the table 3 and table 4, the thickness of the wing
is designed to be 0.1cm, the scales are based on 1cm cord-length for wing section study.
7. 7
Table 3: Analysis of two spar (three cells) wing sections: 1st
wall and 2nd
wall indicate the position walls are placed
from the leading edge,under the thicknesscolumn, the first number is the thickness of the 1st
wall,and the second
number is the thicknessof the 2nd
wall.
From the table 3, we see the calculation for the straight wing matches with our analysis
for a swept forward wing in the following way: With two equally thick cell walls, when the 2nd
wall is place at 0.7cm, it gives us lower max stress. [Note that all locations and thicknesses
presented for the matlab code are in terms of a cord length of 1cm.] Since the twisting is very
similar in both cases, we decided to keep studying the case of first one. When we increased the
thickness of the first wall to 0.025cm, the stress, displacement, and twist decreases. We found
that past this point, increasing the thickness will not yield better results.
Table 4: Analysis of three spar (four cells) wing sections:1st
wall, 2nd
wall,and 3rd
wall indicate the position walls
are placed from the leading edge,under the thickness column, the first number, second number, third number,
represent the thicknessof 1st
wall, 2nd
wall,3rd
wall,and one number means same thickness of the three walls. The
design has refined mesh only when it is indicated.
For the table 4, we did same thing similar to what we did in table 3. We compared the
best stiffness wing section designs, and choose the better one to continue study. Since the 3-wall
design gives us better results, we give up the 2-wall design, so at this time, we have decide the
wall position to at (0.1cm, 0.4cm, 0.7cm), and the next step is to decide the wall thicknesses. We
get very similar result between using thickness of (0.025, 0.01, 0.01) and thickness of (0.035,
0.01, 0.01), so we made refined mesh for both to compare and made our decision of choosing
(0.025, 0.01, 0.01). We can have a look at the thickness (0.025, 0.02, 0.01), in which we increase
the thickness of the center spar resulting in higher stress on the wing. This might be because of
higher twist (displacement difference is larger comparing to other two designs). Adding more
materials backward might have moved the shear center backward and caused higher twist.
In order to move the shear center of the wing forward, it is apparent that the front spar
should be bulkier than the rear spars. But when the thickness of the front spar is increased to
0.035cm, we see in the refined mesh part the stress is increased, but displacement difference is
8. 8
smaller compared to the design with 0.025cm-thickness (smaller twist, forward shear center.
This may occur because of the increased weight causing larger bending moment which leads to
higher stress, stress equals to Mc/I. So we need to keep in mind the side effect of weight when
we move forward.
Part IV --- Analysis of Wing with Ribs
Since the locations of the spars are decided, we calculate the lifting force to be 27N using
the speed of 75mph, 10-deg angle attack with the lift equation. For the following study we will
keep using 27N as applied force and analysis will be based on refined mesh at the wing end since
that is place the maximum stress will be. Throughout this part of analysis, the wing tip is closed
with one solid rib. The analysis result will be shown in table 5. The thickness of the rib is 0.5cm,
and the scales are based on 40cm wingspan.
Table 5: rib0, rib1, rib 2, and rib3 each represent different rib designs, the numbers under the 1rib,2 rib, 3 rib are
the location ofthe ribs from the wing end, there is one with on rib at the wing end as it indicated,the last two
analysishas four ribs in total with one rib at the wing end.
Along the study, we see that displacement difference doesn’t differ a lot from each other
comparing to the output of the max stress,so we want to focus on stress analysis on this part. From the
analysis, we see that adding three solid ribs does help to decrease the stress a lot, but if we take away the
rib at the wing end which is the most critical place, the stress goes up a lot even compared to the design
with no ribs. This indicates that ribs at wrong positions only increase weight which will cause higher
bending moment leading to higher max stress. To verify the effect of bending moment and to compare
designs with three ribs to those with four ribs, we produced two four-rib designs, which are shown at the
bottom part of the table 5. When the ribs are moved closer to the wing tip, the stress goes up a lot because
it moves the center of the weight further away from the wing end. Moment = force*distance, so with the
same amount of weight, larger the distance gives us higher bending moment. So we made our decision of
not putting ribs too far away from the wing end.
Before we think about the position of ribs, we should consider the design of the ribs themselves.
The last two studies they are done using the best rib design we have found, rib3. In order to determine the
final rib locations, we compared all of our designs. By comparing the results of the last three designs
9. 9
which all used rib3 (shown in table 5), we decided to use only two ribs at the location of 9cm, 16cm from
the wing end which gives us the lowest stress. For the rib design, the hollow parts are in shape of square
to maximize the empty area with fillets on the corner to avoid stress concentration. The rib designs are
shown in the Figure 4, and final design on the Figure 5.
a)
b)
Figure 4: rib design: a)rib 0, b) rib2
Figure 5: rib3, final rib design for laser cut, with the leading and trailing part trimmed to add in supporting
material during the assembly process.
The rib 1 is very similar to rib 0, just increasing the area of each hole, and we found that
increasing area does help to reduce the stress a lot. This might be because of the reducing weight leading
to less bending moment. So for the rib2, we increase the hole-areas even more by merging all the small
holes into one big hole, but the result doesn’t go as well as we thought they would. Even though the
bending moment decreased,the inertia of the rib is decreased in rib2. Since stress equals to
Moment*c/inertia, the smaller the inertia, the larger the stress will be. We need to find the design gives us
a lower moment, but a larger inertia. Next, we separated the hole on the center into three holes we
designed in rib1, shown in the Figure 5, as our final design, which gives us the lowest stress and twist.
Part V --- Final design
The pictures in this section were taken after we decided the final design. The results may
be a little different, from the data shown in table 5, and the material properties of the design will
be shown in Appendix C.
a)
11. 11
c)
Figure 6: final design results: a) displacement plot,b) stress plot, c) stress concentration
Figure 7: wing structure, the first spar (closest spar to the stress concentration) is 1cm longer to
insert into the block
Part VI --- Improvement
12. 12
There are a lot of place that we need to spend more time looking into it, we found that
there are a lot of parts that we should have look more into but didn’t give enough analysis.
1) No analysis done based on varying the thickness of the rib. (Since there is no analysis on
this part, we can’t give strong comments about it)
2) No calculation for the more walls analysis. We have calculation based on 1-wall (which
is not very good comparing to the other two so we didn’t talk about it), 2-wall, 3-wall,
and we have found that as the wall number increased, the stiffness ratio increase which
gives us better result. From the analysis, we also see that 3-wall gives less twist than 2-
wall that increasing the number of walls more might help to more the shear center
forward.
3) On the Part IV, when we found that using three ribs gives us better result than using four
ribs, we chose to use the design of (0cm, 9cm, 16cm) from the wing end because that is
the design we keep using and forgot to study the design of (0cm, 4cm, 16cm), or (0cm,
4cm, 9cm) from the wing end. As we have said that Moment = force*distance, then the
moment will be reduced more by get the ribs closer to the end we have realize this, but
didn’t spend enough time into it.
4) The lift force is calculated based on 75mph, but during the completion, we found the
speed to be larger than 75mph.
Appendix A: Gottingen 398 Cross-Section
15. 15
xnew=[0:xspacing:1];
ytopnew=zeros(1,1/xspacing+1);
ybottomnew=zeros(1,1/xspacing+1);
d=0;
%Create new x and y coords spaced according to xspacing values
for i=1:1/xspacing+1
for j=1:length(x)
if x(j)==xnew(i)
ytopnew(i)=ytop(j);
ybottomnew(i)=ybottom(j);
break
elseif xnew(i)>x(j) && xnew(i)<x(j+1) %linearly interpolate to
find new y coords
ytopnew(i)=(ytop(j+1)-ytop(j))*(xnew(i)-x(j))/(x(j+1)-
x(j))+ytop(j);
ybottomnew(i)=(ybottom(j+1)-ybottom(j))*(xnew(i)-
x(j))/(x(j+1)-x(j))+ybottom(j);
break
end
end
d(i)=ytopnew(i)-ybottomnew(i);
end
%xloc=round(xloc,3);
xnum=xloc/xspacing;
D=zeros(1,length(xloc));
%Calculate height of cell walls
for i=1:length(xloc)
D(i)=d(round(xnum(i)+1));
end
n=1;
Atot=0;
Stot=0;
A=zeros(1,length(xloc)+1);
S=zeros(1,length(xloc)+1);
%Calculate cell areas and top+bottom wall lengths
for i=1:round(1/xspacing)
if n<=length(xloc)
if i==round(xnum(n)+1)
n=n+1;
end
end
a(i)=((ytopnew(i)-ybottomnew(i))+(ytopnew(i+1)-
ybottomnew(i+1)))/2*xspacing;
s(i)=sqrt((ytopnew(i+1)-
ytopnew(i))^2+xspacing^2)+sqrt((ybottomnew(i+1)-ybottomnew(i))^2+xspacing^2);
Atot=Atot+a(i);
Stot=Stot+s(i);
A(n)=A(n)+a(i);
S(n)=S(n)+s(i);
end
C=zeros(length(A),length(A));
%Formulate q matrix
for i=1:length(A)-1
C(i,i)=S(i)/t0+D(i)/t(i);
C(i,i+1)=-D(i)/t(i);
C(i+1,i)=-D(i)/t(i);
17. 17
end
end
Ymax=max(max(Y))
[r,c]=ind2sub(size(Y), find(Y==max(Y(:))));
rc=rc*.05
%maximum improvement over single cell design is 16 percent
%Matrix rc gives list of all wall locations for which rigidity improves by
%at least 16 percent over single cell design
Results: the first two numbers are the locations of the wall and the last number is the rigidity
ratio
rc =
0.0500 0.6500 1.1631
0.0500 0.7000 1.1657
0.0500 0.7500 1.1625
0.1000 0.6000 1.1611
0.1000 0.6500 1.1675
0.1000 0.7000 1.1689
0.1000 0.7500 1.1644
0.1500 0.6500 1.1632
0.1500 0.7000 1.1640
3. Three Spar Locations and Ratios:
clc;
clear all;
xloc1=[.05:.05:.95];
xloc2=[.05:.05:.95];
xloc3=[.05:.05:.95];
n=1;
for i=1:19
for j=1:19
for k=1:19
if xloc1(i)>=xloc2(j) || xloc2(j)>=xloc3(k) || xloc1(i)>=xloc3(k)
Y(i,j,k)=1;
else
Y(i,j,k)=TRigidityFunc(.025,[xloc1(i),xloc2(j),xloc3(k)],[.075 .075 .075]);
if Y(i,j,k)>1.213
rch(n,1)=i; %first spar location
rch(n,2)=j; %second spar location
rch(n,3)=k; %third spar location
rch(n,4)=Y(i,j,k)/0.05; %corresponding Stiffscaled ratio
of locations
n=n+1;
end
18. 18
end
end
end
end
Ymax=max(max(max(Y)));
[r,c,h]=ind2sub(size(Y), find(Y==max(Y(:))));
rch=rch*.05
%maximum improvement over single cell design is 20 percent
%Matrix rch gives list of all wall locations for which rigidity improves by
%at least 21.3 percent over single cell design. 20% had too many results.
Results: the first three numbers are the locations of the wall and the last number is the rigidity
ratio
rch =
0.1000 0.3000 0.7000 1.2130
0.1000 0.3500 0.7000 1.2138
0.1000 0.4000 0.7000 1.2145
0.1000 0.4500 0.7000 1.2141
0.1000 0.4500 0.7500 1.2137
0.1000 0.5000 0.7500 1.2138
0.1500 0.3500 0.7000 1.2130
0.1500 0.4000 0.7000 1.2135