Lect03
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The document discusses the advantages and disadvantages of the finite element method (FEM) in civil engineering. It states that FEM can effectively handle problems with irregular shapes, boundary conditions, and loading conditions. It can also solve problems involving anisotropic and non-linear material and geometric properties that classical methods cannot. However, FEM provides approximate solutions rather than exact ones, requires skill in element selection and modeling, and demands significant computer resources.
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The document discusses the finite element method (FEM), a numerical technique used to solve complex engineering problems. FEM was originally developed for aerospace engineering but is now widely used in civil, mechanical, and electrical engineering. It works by dividing a structure into finite elements and obtaining an approximate solution by analyzing the properties of individual elements and their interaction. The key principles of FEM include using computational methods to solve boundary value problems representing physical structures, with field variables governed by differential equations and boundary conditions specified on the field boundaries.
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1. The document outlines the step-by-step procedure for finite element analysis, which includes: selecting suitable field variables and elements, discretizing the continuum, selecting interpolation functions, finding element properties, assembling global properties, imposing boundary conditions, and making additional calculations.
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Lect06
Nodes are points where basic unknowns are determined in finite element analysis and where elements connect. There are two main types of nodes: external nodes located at element edges or surfaces and shared by multiple elements, and internal nodes located inside a single element. External nodes are further divided into primary nodes at corners or ends, and secondary nodes along edges but not at corners. Internal nodes are specific to each individual element.
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The document discusses the role of finite element method (FEM) in orthodontics. FEM is a numerical technique originally used in structural analysis that has been applied to dental biomechanical research. It allows modeling of complex tooth and bone structures to analyze stress and strain distributions. FEM provides advantages over experimental techniques by allowing 3D modeling, use of actual material properties, and ability to efficiently test different force systems. The document reviews studies applying FEM to orthodontic tooth movement, dental implants, and orthopedic appliances. It also discusses challenges modeling the complex properties of living tissues like bone.Surface Analysis Techniques Feb & April 2013
Surface Analysis Techniques Feb & April 2013USAINS Holding Sdn. Bhd. (wholly-owned by Universiti Sains Malaysia)
Suitable for: 1. Technical Personnel and Decision-Makers are encouraged to participate in this training. 2. DECISION MAKERS: Technical Directors, Managers, Purchasers. 3. TECHNICAL PERSONNEL: Lecturers, Technical Sales, Marketing, Failure Analysis, Research & Development, Quality Control and Assurance, Production Engineers or Technicians. The characteristic of surface and near-surface regions of materials can be characterised by various surface analysis techniques. Applications of many engineering materials are determined by the surface and near-surface structures. Therefore, the well being of this region is essential in order to obtain a pre-required condition for those materials to be applied for a specific application. Typically, failure of engineering products may be traced back to surface/near-surface contamination or surface reconstruction. In order to obtain more information related to the failure, in-sight of these regions need to be exposed. This course is outlined to introduce basic principles of surface science, which serve as an essential foundation to explain the operation concepts and applications of several important surface analysis techniques. Know-how of interpreting the analysis data is also explained in this “easy-to-follow” and “easy-to-understand” training course. With these and the support of brief but sufficient fundamental theories, skill of selecting a relevant technique with respect to its practical engineering usage will be covered. Ultimate goal for this course is to increase level of knowledge in making a correct technical decision to solve surface related issues and transform knowledge into applications.Lecture on Introduction to finite element methods & its contents
The document provides an overview of the Finite Element Method (FEM) course being taught. It discusses:
1. What FEM is and its common application areas like structural analysis, heat transfer, fluid flow.
2. The main steps in FEM including discretization, selecting interpolation functions, developing element matrices, assembling the global matrix, imposing boundary conditions, and solving equations.
3. Different element types like 1D, 2D, and 3D elements and the use of isoparametric formulations.
4. The history of FEM and how it has evolved from being used on mainframe computers to PCs.
Evolutionary Algorithmical Approach for VLSI Physical Design- Placement Problem
Physical layout automation is very important in
VLSI’s field. With the advancement of semiconductor
technology, VLSI is coming to VDSM (Very Deep Sub
Micrometer), and the scale of the random logic IC circuits
goes towards million gates. Physical design is the process of
determining the physical location of active devices and
interconnecting them inside the boundary of the VLSI
chip.The earliest and the most critical stage in VLSI layout
design is the placement. The background is the rectangle
packing problem: given a set of rectangular modules of
arbitrary sizes, place them without overlap on a plane within
a rectangle of minimum area [1], [5]. The VLSI placement
problem is to place the object in the fixed area of die without
overlap and with some cost constrain such as the wire length
and area of the die. The wire length and the area optimization
is the major task in the physical design. We first
introduce about the major technique involved in the algorithm
Fluid-Machinery-1.pdf this document is used for cput lecture in mechanical e...
this document is used for cput lecture in mechanical engineering
Ao04605289295
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Su2010
This document describes a finite element method for modeling complex 3D crack propagation in quasi-brittle materials under static and dynamic loading conditions. The method embeds cohesive elements, which model potential cracks, between solid elements in regions of interest in the initial mesh. Neither remeshing nor predefined crack paths are required. The method was implemented in Abaqus and used to model crack propagation in four concrete structure examples, showing good agreement with experiments or other simulations. The method offers engineers an efficient tool for modeling 3D fracture problems using Abaqus' preprocessing, solving, and postprocessing capabilities.
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01. steps involved, merits, demerits & limitations of fem
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Role of Finite element analysis in orthodontics /certified fixed orthodontic ...
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Role of finite element analysis in orthodontics /certified fixed orthodontic ...
Role of finite element analysis in orthodontics /certified fixed orthodontic ...
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Evolutionary Algorithmical Approach for VLSI Physical Design- Placement Problem
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More from DrASSayyad
Matrix Methods of Structural Analysis
This document contains lecture notes on matrix methods of structural analysis. It discusses three methods for solving systems of linear equations that arise in structural analysis problems - Gauss elimination method, Gauss-Jordan method, and Gauss-Seidel iterative method. For each method, an example problem is provided and solved step-by-step to illustrate the application of the method.
Theory of Plates and Shells
This document provides an overview of basic equations for the theory of plates and shells. It discusses the state of stress and strain at a point, including defining the six independent stress and strain components. It presents the relationships between strain and displacement, and discusses the equilibrium equations relating stress and body forces. Finally, it provides the equations for both Cartesian and cylindrical coordinate systems. The key concepts covered are the fundamental equations that form the basis of plate and shell theory.
Fem class notes
This document contains lecture notes on the finite element method from Dr. Atteshamuddin S. Sayyad. It covers the fundamentals of elasticity theory including assumptions, basic terms like stresses and strains, equilibrium equations, and strain-displacement relationships. The notes provide definitions and equations for normal and shear stresses and strains, the state of stress and strain at a point, and developing the governing equations of equilibrium in three dimensions from an infinitesimal element.
Lect21
1. The document derives the shape functions for a three-noded constant strain triangular (CST) element.
2. It presents the displacement function in terms of nodal displacements using the element connectivity matrix.
3. The shape functions are obtained by relating the displacement function to the nodal displacement terms, resulting in a set of three linear shape functions that describe the displacement across the element in terms of the displacements at its nodes.
Lect20
1) The document derives the shape functions for a two-noded bar element in finite element analysis.
2) It expresses the displacement function in terms of the nodal displacements using the coordinates of the two nodes.
3) The shape functions are obtained by equating the displacement function to the product of the shape function matrix and the nodal displacement vector.
Lect19
This document discusses shape functions in finite element analysis. It explains that shape functions approximate the variation of displacement within an element since the true variation is unknown. Shape functions, also called interpolation functions, are used to replace difficult analytical solutions with easier mathematical functions. Important properties of shape functions are that the magnitude at each node is unity, the number of functions equals the number of nodes, and the sum of functions is always unity. Common methods for deriving shape functions include using polynomials in Cartesian and natural coordinate systems and Lagrange interpolation in natural coordinates.
Lect18
This document introduces 3D elements that can model structural components in three dimensions. It discusses two families of 3D elements: tetrahedrons generated from triangular elements, and parallelepipeds generated from rectangular elements. Common 3D solid elements for finite element analysis include the 4-noded tetrahedron and 8-noded hexahedron/brick. The tetrahedron has 12 degrees of freedom while the hexahedron has 24 degrees of freedom. Displacement functions are provided for both elements. 3D elements can be used for fully 3D analysis and modeling axisymmetric solids.
Lect17
The document discusses natural coordinates, also called area coordinates, for a three-node triangular element in finite element analysis. It defines the natural coordinates (L1, L2, L3) of any point P within the triangle in terms of the Cartesian coordinates of the three nodes and the fractions of the total triangle area (A1, A2, A3) associated with each node. The natural coordinates represent the point P shifted to each node and satisfy the properties L1 + L2 + L3 = 1 and L1, L2, L3 ≥ 0.
Lect16
The document discusses the natural coordinates of a 1D bar element in finite element analysis. It defines the natural coordinate ξ as the ratio of the distance from any point P to the origin, over the maximum distance from the origin to node 2. This yields expressions for ξ at each node. At node 1, ξ = 0, and at node 2, ξ = 1. Therefore, the natural coordinates of a 1D bar element are ξ, which ranges from 0 at node 1 to 1 at node 2.
Lect15
1) The document discusses natural coordinates for a 1D bar element in finite element analysis.
2) It defines the natural coordinates (L1, L2) of any point P on the bar element in terms of the Cartesian coordinates (x1, x2) of the two nodes and the length L of the element.
3) The natural coordinates at node 1 are derived to be (1, 0) and at node 2 to be (0, 1).
Lect14
This document compares the constant strain triangular (CST) element and the linear strain triangular (LST) element in finite element analysis. It states that the CST element has constant strains inside each element but strains are not continuous across boundaries. In contrast, the LST element has linear strains inside each element and is preferred for stress analysis due to its higher accuracy. The document recommends using LST elements over multiple CST elements for better representation of stresses and displacements.
Lect13
This document discusses displacement functions or polynomial functions for various finite elements. It provides examples of the displacement functions for:
1) A two-noded bar element with two degrees of freedom.
2) A three-noded bar element with three degrees of freedom.
3) A two-noded beam element with four degrees of freedom.
4) A constant strain triangular element with six degrees of freedom.
It explains that the displacement functions are selected from Pascal's triangle and include terms for x- and y-coordinates for two-dimensional elements.
Lect12
The document discusses geometric isotropy or invariance in finite element modeling, which means the displacement shapes of an element do not change with a change in the local coordinate system. This can be achieved in 2D modeling by selecting terms on either side of the Pascal's triangle that correspond to the same order. In 3D modeling, geometric invariance requires selecting terms based on the 3D Pascal's triangle.
Lect11
The document discusses three criteria for the convergence of displacement/shape functions in the finite element method:
1) Displacement functions must be continuous and compatible within elements, with no discontinuities between elements.
2) Displacement functions must be capable of representing constant strain states within elements.
3) Displacement functions must be capable of representing rigid body displacements, with elements experiencing no strain and zero nodal forces under rigid body motion.
Lect10
The document discusses the different types of finite elements used in civil engineering. It outlines three main types: 1) 1D elements which are used to analyze trusses, beams, pipes and tubes; 2) 2D elements which are used for plane stress, plane strain and plate bending as well as shell structures; and 3) 3D elements which are used for three-dimensional analysis and axisymmetric solids.
Lect08
The document discusses element aspect ratios in finite element analysis for civil engineering structures. It defines aspect ratio as the ratio of the largest to smallest size of an element. For analysis accuracy, the aspect ratio should be as close to unity as possible. It provides an example of correctly sizing square elements of equal size compared to incorrectly using long rectangular elements.
Lect07
This document discusses effective node numbering schemes for finite element analysis. It explains that effective node numbering should minimize the bandwidth of the stiffness matrix. The bandwidth is calculated as B = (1+D)f, where D is the maximum difference in node numbers between any two connected nodes, and f is the degrees of freedom per node. Several examples are provided to demonstrate calculating the bandwidth for different node numbering approaches applied to structures like rectangular slabs and trusses. Effective node numbering reduces computation time by producing a banded, sparse stiffness matrix.
Lect04
The document discusses applications of the finite element method (FEM) in various engineering fields. It lists applications of FEM in civil engineering such as analyzing structures like bars, trusses, beams and frames; earthquake analysis; and bending, buckling and vibration analysis of beams and plates. It also lists applications of FEM in mechanical engineering, aerospace engineering, medical engineering, and electrical engineering.
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Lect03
- 1. Dr. A. S. Sayyad Professor & Head Department of Structural Engineering Sanjivani College of Engineering, Kopargaon 423603. (An Autonomous Institute, Affiliated to Savitribai Phule Pune University, Pune) Finite Element Method In Civil Engineering Advantages and Disadvantages of FEM
- 2. 1. Finite element method is effectively applicable to problems involving irregular shape, irregular boundary condition and irregular loading conditions. 2. For anisotropic material properties, solution by classical method is very difficult. FEM can handle such structures without any difficulty. 3. Material non-linearity and geometric non- linear problems cannot handle by classical methods. There is no difficulty in FEM to handle such problem. 4. FEM superior to irregular problems, for regular problems classical methods are best solution Advantages of FEM
- 3. 1. In classical method exact solution is obtained whereas in FEM approximate solution is obtained. 2. This technique depends upon skill designer in assuming element type, number of nodes and displacement fields etc. 3. Still adequate for several problems such as; cracking behaviour, bond failure, problems of composite materials. 4. It requires large amount of computer memory and computational time to obtained results. Disadvantages of FEM Question: What are the advantages and disadvantages of FEM? Explain