Buckling of a carbon nanotube embedded in elastic medium via nonlocal elastic...IRJESJOURNAL
Abstract:- Buckling analysis of a carbon nanotube (CNT) embedded in Pasternak’s medium is investigated. Eringen’s nonlocal elasticity theory in conjunction with the first-order Donell’s shell theory is used. The governing equilibrium equations are obtained and solved for CNTs subjected to mechanical loads and embedded in Winkler-Pasternak’s medium. Effects of nonlocal parameter, radius and length of CNT, as well as the foundation parameters on buckling of CNT are investigated. Comparison with the available results is made.
Buckling of a carbon nanotube embedded in elastic medium via nonlocal elastic...IRJESJOURNAL
Abstract:- Buckling analysis of a carbon nanotube (CNT) embedded in Pasternak’s medium is investigated. Eringen’s nonlocal elasticity theory in conjunction with the first-order Donell’s shell theory is used. The governing equilibrium equations are obtained and solved for CNTs subjected to mechanical loads and embedded in Winkler-Pasternak’s medium. Effects of nonlocal parameter, radius and length of CNT, as well as the foundation parameters on buckling of CNT are investigated. Comparison with the available results is made.
This Report presents a review of the definition of the equivalent crack concept by defining the relationship between two correlated theories, which are fracture mechanics and damage mechanics based on Mazars static damage model and derived in the framework of the thermodynamics of irreversible processes, an energetic equivalence between the two descriptions is proposed. This paper also presents an example of combined damage and fracture calculation on a concrete specimen, the energy consumption during crack propagation, modelled with damage mechanics, is computed. Finally, the paper provide a comparison for the fracture energy according to the damage model with experiments and linear elastic fracture mechanics
Comparative study of results obtained by analysis of structures using ANSYS, ...IOSR Journals
The analysis of complex structures like frames, trusses and beams is carried out using the Finite
Element Method (FEM) in software products like ANSYS and STAAD. The aim of this paper is to compare the
deformation results of simple and complex structures obtained using these products. The same structures are
also analyzed by a MATLAB program to provide a common reference for comparison. STAAD is used by civil
engineers to analyze structures like beams and columns while ANSYS is generally used by mechanical engineers
for structural analysis of machines, automobile roll cage, etc. Since both products employ the same fundamental
principle of FEM, there should be no difference in their results. Results however, prove contradictory to this for
complex structures. Since FEM is an approximate method, accuracy of the solutions cannot be a basis for their
comparison and hence, none of the varying results can be termed as better or worse. Their comparison may,
however, point to conservative results, significant digits and magnitude of difference so as to enable the analyst
to select the software best suited for the particular application of his or her structure.
Implementation Of Geometrical Nonlinearity in FEASTSMTiosrjce
Analysis of the structures used in aerospace applications is done using finite element
method. These structures may face unexpected loads because of variable environmental situations.
These loads could lead to large deformation and inelastic manner. The aim of this research is to
formulate the finite elements considering the effect of large deformation and strain. Here total
Lagrangian method is used to consider the effect of large deformation. After deriving required
relations, implementation of formulated equation is done in FEASTSMT(Finite Element Analysis of
Structures - Substructured and Multi-Threading). .Newton-Raphson method was utilized to solve
nonlinear finite element equations. The validation is carried out with the results obtained from the
Marc Software.
A study on mhd boundary layer flow over a nonlinear stretching sheet using im...eSAT Journals
Abstract
The problem of the MHD boundary layer flow of an incompressible viscous fluid over a non-linear stretching sheet is discussed.
Using similarity transformation governing equations are transformed in to nonlinear ordinary differential equation. The Implicit finite
difference Keller box method is applied to find the numerical solution of nonlinear differential equation. Graphical results of fluid
velocity have been presented and discussed for the related parameters.
Keywords: MHD, boundary layer, nonlinear differential equations, and Keller box method
MODELING OF MANUFACTURING OF A FIELDEFFECT TRANSISTOR TO DETERMINE CONDITIONS...antjjournal
In this paper we introduce an approach to model technological process of manufacture of a field-effect
heterotransistor. The modeling gives us possibility to optimize the technological process to decrease length
of channel by using mechanical stress. As accompanying results of the decreasing one can find decreasing
of thickness of the heterotransistors and increasing of their density, which were comprised in integrated
circuits.
Unconventional phase transitions in frustrated systems (March, 2014)Shu Tanaka
Presentation file using the workshop which was held at the University of Tokyo (March 26, 2014). The presentation was based on two papers:
- Physical Review B Vol. 87, 214401 (2013)
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.87.214401
(preprint: http://arxiv.org/abs/1209.2520)
(A brief explanation: http://www.slideshare.net/shu-t/prb-87214401slideshare)
- Physical Review E Vol. 88, 052138 (2013)
http://journals.aps.org/pre/abstract/10.1103/PhysRevE.88.052138
(preprint: http://arxiv.org/abs/1308.2467)
(A brief explanation: http://www.slideshare.net/shu-t/interlayerinteraction-dependence-of-latent-heat-in-the-heisenberg-model-on-a-stacked-triangular-lattice-with-competing-interactions)
2014年3月26日に東京大学で開催された「統計物理学の新しい潮流」での講演スライドです。この講演は、以下の2つの論文に関係するものです。
- Physical Review B Vol. 87, 214401 (2013)
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.87.214401
(preprint: http://arxiv.org/abs/1209.2520)
(A brief explanation: http://www.slideshare.net/shu-t/prb-87214401slideshare)
- Physical Review E Vol. 88, 052138 (2013)
http://journals.aps.org/pre/abstract/10.1103/PhysRevE.88.052138
(preprint: http://arxiv.org/abs/1308.2467)
(A brief explanation: http://www.slideshare.net/shu-t/interlayerinteraction-dependence-of-latent-heat-in-the-heisenberg-model-on-a-stacked-triangular-lattice-with-competing-interactions)
Numerical simulation on laminar convection flow and heat transfer over a non ...eSAT Journals
Abstract
A numerical algorithm is presented for studying laminar convection flow and heat transfer over a non-isothermal horizontal plate.
plate temperature Tw varies with x in the following prescribed manner:
T T Cx w
n 1
where C and n are constants. By means of similarity transformation, the original nonlinear partial differential equations of flow
are transformed to a pair of nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and
integrated using Newton Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical
analysis in Matlab environment. Velocity, and temperature profiles for various Prandtl number and n are illustrated graphically.
Flow and heat transfer parameters are derived. The results of the present simulation are then compared with experimental data in
literature with good agreement.
Keywords: Free Convection, Heat Transfer, Non-isothermal Horizontal Plate, Matlab, Numerical Simulation.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
This Report presents a review of the definition of the equivalent crack concept by defining the relationship between two correlated theories, which are fracture mechanics and damage mechanics based on Mazars static damage model and derived in the framework of the thermodynamics of irreversible processes, an energetic equivalence between the two descriptions is proposed. This paper also presents an example of combined damage and fracture calculation on a concrete specimen, the energy consumption during crack propagation, modelled with damage mechanics, is computed. Finally, the paper provide a comparison for the fracture energy according to the damage model with experiments and linear elastic fracture mechanics
Comparative study of results obtained by analysis of structures using ANSYS, ...IOSR Journals
The analysis of complex structures like frames, trusses and beams is carried out using the Finite
Element Method (FEM) in software products like ANSYS and STAAD. The aim of this paper is to compare the
deformation results of simple and complex structures obtained using these products. The same structures are
also analyzed by a MATLAB program to provide a common reference for comparison. STAAD is used by civil
engineers to analyze structures like beams and columns while ANSYS is generally used by mechanical engineers
for structural analysis of machines, automobile roll cage, etc. Since both products employ the same fundamental
principle of FEM, there should be no difference in their results. Results however, prove contradictory to this for
complex structures. Since FEM is an approximate method, accuracy of the solutions cannot be a basis for their
comparison and hence, none of the varying results can be termed as better or worse. Their comparison may,
however, point to conservative results, significant digits and magnitude of difference so as to enable the analyst
to select the software best suited for the particular application of his or her structure.
Implementation Of Geometrical Nonlinearity in FEASTSMTiosrjce
Analysis of the structures used in aerospace applications is done using finite element
method. These structures may face unexpected loads because of variable environmental situations.
These loads could lead to large deformation and inelastic manner. The aim of this research is to
formulate the finite elements considering the effect of large deformation and strain. Here total
Lagrangian method is used to consider the effect of large deformation. After deriving required
relations, implementation of formulated equation is done in FEASTSMT(Finite Element Analysis of
Structures - Substructured and Multi-Threading). .Newton-Raphson method was utilized to solve
nonlinear finite element equations. The validation is carried out with the results obtained from the
Marc Software.
A study on mhd boundary layer flow over a nonlinear stretching sheet using im...eSAT Journals
Abstract
The problem of the MHD boundary layer flow of an incompressible viscous fluid over a non-linear stretching sheet is discussed.
Using similarity transformation governing equations are transformed in to nonlinear ordinary differential equation. The Implicit finite
difference Keller box method is applied to find the numerical solution of nonlinear differential equation. Graphical results of fluid
velocity have been presented and discussed for the related parameters.
Keywords: MHD, boundary layer, nonlinear differential equations, and Keller box method
MODELING OF MANUFACTURING OF A FIELDEFFECT TRANSISTOR TO DETERMINE CONDITIONS...antjjournal
In this paper we introduce an approach to model technological process of manufacture of a field-effect
heterotransistor. The modeling gives us possibility to optimize the technological process to decrease length
of channel by using mechanical stress. As accompanying results of the decreasing one can find decreasing
of thickness of the heterotransistors and increasing of their density, which were comprised in integrated
circuits.
Unconventional phase transitions in frustrated systems (March, 2014)Shu Tanaka
Presentation file using the workshop which was held at the University of Tokyo (March 26, 2014). The presentation was based on two papers:
- Physical Review B Vol. 87, 214401 (2013)
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.87.214401
(preprint: http://arxiv.org/abs/1209.2520)
(A brief explanation: http://www.slideshare.net/shu-t/prb-87214401slideshare)
- Physical Review E Vol. 88, 052138 (2013)
http://journals.aps.org/pre/abstract/10.1103/PhysRevE.88.052138
(preprint: http://arxiv.org/abs/1308.2467)
(A brief explanation: http://www.slideshare.net/shu-t/interlayerinteraction-dependence-of-latent-heat-in-the-heisenberg-model-on-a-stacked-triangular-lattice-with-competing-interactions)
2014年3月26日に東京大学で開催された「統計物理学の新しい潮流」での講演スライドです。この講演は、以下の2つの論文に関係するものです。
- Physical Review B Vol. 87, 214401 (2013)
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.87.214401
(preprint: http://arxiv.org/abs/1209.2520)
(A brief explanation: http://www.slideshare.net/shu-t/prb-87214401slideshare)
- Physical Review E Vol. 88, 052138 (2013)
http://journals.aps.org/pre/abstract/10.1103/PhysRevE.88.052138
(preprint: http://arxiv.org/abs/1308.2467)
(A brief explanation: http://www.slideshare.net/shu-t/interlayerinteraction-dependence-of-latent-heat-in-the-heisenberg-model-on-a-stacked-triangular-lattice-with-competing-interactions)
Numerical simulation on laminar convection flow and heat transfer over a non ...eSAT Journals
Abstract
A numerical algorithm is presented for studying laminar convection flow and heat transfer over a non-isothermal horizontal plate.
plate temperature Tw varies with x in the following prescribed manner:
T T Cx w
n 1
where C and n are constants. By means of similarity transformation, the original nonlinear partial differential equations of flow
are transformed to a pair of nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and
integrated using Newton Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical
analysis in Matlab environment. Velocity, and temperature profiles for various Prandtl number and n are illustrated graphically.
Flow and heat transfer parameters are derived. The results of the present simulation are then compared with experimental data in
literature with good agreement.
Keywords: Free Convection, Heat Transfer, Non-isothermal Horizontal Plate, Matlab, Numerical Simulation.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
All of material inside is un-licence, kindly use it for educational only but please do not to commercialize it.
Based on 'ilman nafi'an, hopefully this file beneficially for you.
Thank you.
this is presentation on " skewed plate problem " which is related to advanced mechanic of material of subject.here explain about principle,method and approximation function with also steps wise for solving problem in Ritz method and discuss about the skewed plate problem. included conclusion and references.
GDQ SIMULATION FOR FLOW AND HEAT TRANSFER OF A NANOFLUID OVER A NONLINEARLY S...AEIJjournal2
This paper presents the generalized differential quadrature (GDQ) simulation for analysis of a nanofluid
over a nonlinearly stretching sheet. The obtained governing equations of flow and heat transfer are
discretized by GDQ method and then are solved by Newton-Raphson method. The effects of stretching
parameter, Brownian motion number (Nb), Thermophoresis number (Nt) and Lewis number (Le), on the
concentration distribution and temperature distribution are evaluated. The obtained results exhibit that
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
FINGERPRINTS IMAGE COMPRESSION BY WAVE ATOMScsandit
The fingerprint images compression based on geometric transformed presents important
research topic, these last year’s many transforms have been proposed to give the best
representation to a particular type of image “fingerprint image”, like classics wavelets and
wave atoms. In this paper we shall present a comparative study between this transforms, in
order to use them in compression. The results show that for fingerprint images, the wave atom
offers better performance than the current transform based compression standard. The wave
atoms transformation brings a considerable contribution on the compression of fingerprints
images by achieving high values of ratios compression and PSNR, with a reduced number of
coefficients. In addition, the proposed method is verified with objective and subjective testing.
Smart TV Buyer Insights Survey 2024 by 91mobiles.pdf91mobiles
91mobiles recently conducted a Smart TV Buyer Insights Survey in which we asked over 3,000 respondents about the TV they own, aspects they look at on a new TV, and their TV buying preferences.
Search and Society: Reimagining Information Access for Radical FuturesBhaskar Mitra
The field of Information retrieval (IR) is currently undergoing a transformative shift, at least partly due to the emerging applications of generative AI to information access. In this talk, we will deliberate on the sociotechnical implications of generative AI for information access. We will argue that there is both a critical necessity and an exciting opportunity for the IR community to re-center our research agendas on societal needs while dismantling the artificial separation between the work on fairness, accountability, transparency, and ethics in IR and the rest of IR research. Instead of adopting a reactionary strategy of trying to mitigate potential social harms from emerging technologies, the community should aim to proactively set the research agenda for the kinds of systems we should build inspired by diverse explicitly stated sociotechnical imaginaries. The sociotechnical imaginaries that underpin the design and development of information access technologies needs to be explicitly articulated, and we need to develop theories of change in context of these diverse perspectives. Our guiding future imaginaries must be informed by other academic fields, such as democratic theory and critical theory, and should be co-developed with social science scholars, legal scholars, civil rights and social justice activists, and artists, among others.
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...Ramesh Iyer
In today's fast-changing business world, Companies that adapt and embrace new ideas often need help to keep up with the competition. However, fostering a culture of innovation takes much work. It takes vision, leadership and willingness to take risks in the right proportion. Sachin Dev Duggal, co-founder of Builder.ai, has perfected the art of this balance, creating a company culture where creativity and growth are nurtured at each stage.
Software Delivery At the Speed of AI: Inflectra Invests In AI-Powered QualityInflectra
In this insightful webinar, Inflectra explores how artificial intelligence (AI) is transforming software development and testing. Discover how AI-powered tools are revolutionizing every stage of the software development lifecycle (SDLC), from design and prototyping to testing, deployment, and monitoring.
Learn about:
• The Future of Testing: How AI is shifting testing towards verification, analysis, and higher-level skills, while reducing repetitive tasks.
• Test Automation: How AI-powered test case generation, optimization, and self-healing tests are making testing more efficient and effective.
• Visual Testing: Explore the emerging capabilities of AI in visual testing and how it's set to revolutionize UI verification.
• Inflectra's AI Solutions: See demonstrations of Inflectra's cutting-edge AI tools like the ChatGPT plugin and Azure Open AI platform, designed to streamline your testing process.
Whether you're a developer, tester, or QA professional, this webinar will give you valuable insights into how AI is shaping the future of software delivery.
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
This presentation was delivered at K8SUG Singapore. See https://feryn.eu/presentations/accelerate-your-kubernetes-clusters-with-varnish-caching-k8sug-singapore-28-2024 for more details.
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
"Impact of front-end architecture on development cost", Viktor TurskyiFwdays
I have heard many times that architecture is not important for the front-end. Also, many times I have seen how developers implement features on the front-end just following the standard rules for a framework and think that this is enough to successfully launch the project, and then the project fails. How to prevent this and what approach to choose? I have launched dozens of complex projects and during the talk we will analyze which approaches have worked for me and which have not.
Let's dive deeper into the world of ODC! Ricardo Alves (OutSystems) will join us to tell all about the new Data Fabric. After that, Sezen de Bruijn (OutSystems) will get into the details on how to best design a sturdy architecture within ODC.
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...DanBrown980551
Do you want to learn how to model and simulate an electrical network from scratch in under an hour?
Then welcome to this PowSyBl workshop, hosted by Rte, the French Transmission System Operator (TSO)!
During the webinar, you will discover the PowSyBl ecosystem as well as handle and study an electrical network through an interactive Python notebook.
PowSyBl is an open source project hosted by LF Energy, which offers a comprehensive set of features for electrical grid modelling and simulation. Among other advanced features, PowSyBl provides:
- A fully editable and extendable library for grid component modelling;
- Visualization tools to display your network;
- Grid simulation tools, such as power flows, security analyses (with or without remedial actions) and sensitivity analyses;
The framework is mostly written in Java, with a Python binding so that Python developers can access PowSyBl functionalities as well.
What you will learn during the webinar:
- For beginners: discover PowSyBl's functionalities through a quick general presentation and the notebook, without needing any expert coding skills;
- For advanced developers: master the skills to efficiently apply PowSyBl functionalities to your real-world scenarios.
How world-class product teams are winning in the AI era by CEO and Founder, P...
25 johnarry tonye ngoji 250-263
1. Innovative Systems Design and Engineering www.iiste.org
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol 2, No 4, 2011
Acceleration-Displacement Ratio Transform of Differentials
for Transverse Plates and Constant Stiffness Buckling
Solution.
Tonye Ngoji Johnarry
Department of Civil Engineering
Rivers State University of Science &Technology
PMB 5080, Port-Harcourt , Nigeria
Tel:384 08033101232 ,Email: tnjohnarry@yahoo.com
The research was financed by Rootway Academy Services Limited. No 2011-RWR-2
Abstract
The existing classical plate solution expands the load function in Fourier(trigonometric) series to be in
tune with the partial differentials representing loading. In this presentation, constant point-wise values
of the differentials are sought in conformity with constant rate of loading. Faster exact results are
demonstrated by this new method for both lateral loading and buckling. The subject is relevant for
developing technologies on account of huge constructional works in office and apartment buildings,
ships, oil pipe-lines, oil reservoirs and platforms ,beams-and-plates bridges and similar events. The
method is shown to lead to buckling solutions by the constant initial elastic stiffness procedure ,
perhaps, for the first time .
Keywords : acceleration; displacement; ratio; envelops; beam; plate ;buckling ;stiffness matrix .
1. Introduction:
Civil, environmental and specialized industrial construction-works are every-day activities and plate
bending ,buckling of plates and frames in buildings, air-crafts, bridge-works, and many other areas call
for fast ,accurate and simplified design-analysis. Timoshenko and Woinowsky-Krieger,(1959), studied
the strength of plates and shells and their publication has continued to serve as reference compendium
to researchers. The connection of beams and columns to make load-carrying structures carries with it
the need to continue to study the phenomenon of buckling failure. Wood (1974),Horne(1975), Cheong-
Siat- Moi (1977), Mottram(2008) give relatively recent effective opinions on buckling of frames. What
is, remarkably, absent in the literature is the study of buckling by the constant elastic stiffness matrix;
rather in the existing method ,the stiffness matrix is reformed by stability functions adjustments of the
slope-deflection equations according to the growth of axial forces. Johnarry (2009,2011) showed how
250
2. Innovative Systems Design and Engineering www.iiste.org
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol 2, No 4, 2011
the acceleration-displacement transform of partial differentials can successfully lead to a constant
stiffness solution of buckling problems in bars and frames .All solutions are ,first ,with respect to
curvatures and moments relative to support values and these resolve to final solution values when any
tuning support fixing curvatures/moments have been accounted for.
The method of matrix analysis of frames and the finite element analysis of continuums are well known.
In the present computer implementation of acceleration-displacement transform, bending moments are
interpreted as accelerations (and they are) and where gravity loads appear in the final stiffness
equation, [K].{ d }= {F} , the nodal bending moments are substituted .By successive approximation,
after some two or three iterations a steady-state situation is achieved and that is the objective. The
relative acceleration-displacement-ratio must be point-wise constant, as much as feasible; that is
resonance.
The method readily computes the fundamental frequencies of structures/frames (not shown here,
Johnarry ,2009). A new and simpler buckling instability criterion is, by this method, defined.
2. Plate Solution by Acceleration-displacement Ratio Transform:
The flexure of the plate is described by the bi-harmonic equation,
D[∂4w / ∂x 4 + 2 ∂4w / ∂x2∂y2 + ∂4w / ∂y4] = q …..(2.1)
= D(w,xxxx + 2 w,xxyy +w,yyyy ) = q ;alternate statement of Eq.2.1
The equation can be solved as, (D=flexural rigidity of thin plate.)
D. J. w = q ; or w = (q/D)/ J ….. (2.2)
This is a direct opposite of the Fourier series transformation of the load method in that each of the
differentials in Eq.2.1 is made to have a point-wise constant value over the domain .
Transform into acceleration-displacement ratio, -‘Rad =Rxx.,Ryy.,Rxy.,’ thus, (χ =∂2w/∂x2 .)
∂4w/ ∂x4 = Jxx.[ (∂2w/∂x2) – (∂2w/∂x2)0] /w . =Jxx .Rxx (2.3)
So, multiply through by ‘w’ and integrate,
∫∫(∂4w/ ∂x4) w ∂x ∂y = Jxx ∫∫ (χ - χ0) ∂x∂y …..(2.4)
251
3. Innovative Systems Design and Engineering www.iiste.org
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol 2, No 4, 2011
For the all-round - ss case of a plate, take
w = ∑ ∑ Amn (sin m π x/a)sin n π y/b … (2.5)
∞ ∞
= ∑ ∑ Amn Sx.Sy.
m=1 n=1
Introducing Eq.2.5 for Eq.2.4, we have
Jxx = Amn m3 n π4 /16a2 …..(2.6)
Also
∂4w/∂y4 = Jyy (∂2w/∂y2) / w
Jyy = Amn m n3 π 4 / 16b2
2.1.1 Twist Transform :
If it were possible,
w,xxyy. = Jxy. (w,xy.)relative /w
The twisting curvature (w,xy,rel) integrate to zero and is unsuitable ,vis-à-vis the ‘LHS’. Twists are
complements of normal shapes and lack independence and can be related to the normal shapes. Find an
alternate equivalent twist shape function, G,w,xxyy-eff
G.w,xxyy-eff. = Kt. [Gw,xxxx. + Gw,yyyy. ] …………(2.7)
Choose ‘Kt’ so that the maximum relative ordinates on both sides of Eq.2.8 are equal.
Relative accelerations form the basis of the analysis.
Kt. = [ Gw,xxyy]rel,max. / [Gw,xxxx + Gw,yyyy, ]rel,max. (2.8)
In the ss-case, ‘Kt’ = 1/2 .More studies are necessary here.
Gw,xxyy,eff .= Kt .[Gw,xxxx + Gw,yyyy ] = Jxy . ;;(constant contribution);
∫∫ Gw,xxyy,eff. w ∂x∂y = Jxy.. ∫∫ (1.0) w ∂x∂y ………………………………… (2.8)
[(m2)(n2)(π4)/(a2.b2)] ∫∫(Sx)2(Sy)2 .∂x∂y = (Jxy) ∫∫ (Sx)(Sy) ∂x∂y
Jxy = Amn m3 n3 π 6 /(16a2 b2)
Eq.2.1 now becomes
252
4. Innovative Systems Design and Engineering www.iiste.org
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol 2, No 4, 2011
D [ Jxx( ∂2 w / ∂x2) / w + 2 Jxy . +Jyy (∂2w / dy2) / w] = q ……….. (2.9)
When reduced, we have
Amn [π6/16] m n ( m2/a2 + n2 / b2)2 = q / D …………. (2.10)
Amn = ∑ ∑ (16q /D) (π6 m n (m2 /a2 + n2 / b2)2 . ……………………. .(2.11)
This is an exact amplitude expression in Timoshenko&Krieger (1959) and so, all results of
displacements and moments are as in that citation.
wi = Ac Sx.Sy. = 0.00416qa4 /D, for m = 1, n = 1; x = a/2; y = b/2
which is the exact known result , for the fundamental.
Taking additionally, m=1,n=3;m=3,n=1;m=3,n=3; wc. =0.00406 qa4/D
2.2 The Point Load Case :
From Eq.2.9 multiplied by ‘w’ for integration
D∫∫ [ Jxx ∂2w / ∂x2 + 2Jxy w + Jyy ∂2w/ ∂y2] = q* w = ∫∫ q*∂x∂yAmn.Sx.Sy. … (2.12)
‘q*’ only exists at an isolated center area where the total load is ’P’ with maximum
displacement, wp .=A.*mn Integrate over area so that,
∫∫ (q*) ∂x∂y (wp) = P (Amn )Sx.Sy .………… (2.13)
This allows potentials to be compared on both sides of Eq.2.9
DAmn .Σ Σ [ Jxx (π2 m2) (4ab )/(a2mnπ2 ) + Jyy (π2n2) (4ab)/(b2 mn π2 ) +
2Jxy .(4) a b/(m nπ2 )] = Σ Σ (q* ∂x∂y wc,mn. )(Sx.Sy.)norm = (P)(Sx.Sy.)norm …… (2.14)
Amn =(16P/D/π4)Sx.Sy./[ m3 n (4mb)/(a2 n a) + mn3 (8na)/(b2.mb)+4m2..n2./(ab)] .. (2.15)
w = Σ Σ Amn. Sx.Sy. ;(put in Amn. and complete the solution)
w = [(4P/D/π4) (Sx.Sy.)2] / [m4b /a . + 2m2.n2.a/b + n4.a3/b3] /a2 .…. (2.16)
w1,1 = P a2 ./97.4 = 0.0103 P a2 /D ;;(exact as in Ref -1, for m=n=1);
w1,3. = 0.00041 = w3,1. ;w1,6=0.00006075 =w1,6 ;w3,3=0.000127 ;So,
2
w1,1;1,3;3,1,1,6;6,1;3,3. = 0.01135 Pa . /D ;(exact,0.0116-Ref-1))
253
5. Innovative Systems Design and Engineering www.iiste.org
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol 2, No 4, 2011
(χx ) = D ∂2w/ ∂2x ……………. (2.17)
Alternatively find curvatures/moments from the eventual displacement relation,
w = wc. Sin πx/a .Sin πy/b. (wc.= final central displacement=known) …
( χc)x. = 0.01135(π2) P = 0.112
Allowing for poison’s ratio of ‘0.3’ then ‘mc’= 0.1456 P = P/6.87; almost final but no comparable
exact result source. The present method finds exact results of displacements and credible results for
bending moments, if the point load does not cause immediate collapse.
2.3 The All-round Clamped Plate Under Uniform Loading
The deflection function, side lengths ,a,b ,in X and Y
wi =Amn. Σ Σ (cos mπx/a -1) (cos nπy/b -1 ) (2.18)
meets all boundary conditions,Fig.1f
put , (cos mπ x/a ) = Cx ; (cos nπ y/b )= Cy .
Transform, employing relative curvature for tuning,
(∂w4 / ∂ x4) = Jxx. [(∂w2 /∂x2)-(∂2w/∂x2.) 0.] / w =(Jxx)(Rad)xx
The acceleration-displacement ratio,(Rad) must have a point-wise constant ratio ,hence employ relative
curvatures (χr)=(χi)-(χ0) to achieve it. Tuning, forces the moment diagram to emulate deflection
diagram, presenting a point-wise constant ratio, (Rad), between the two. Tuning, produces buckling-
compliant curvatures.
(∂2w/∂x2 )relative . = (χ) - (χ0) = (Rxx ) w …………… (2.19)
This transformation, in effect, compares the envelops of the acceleration and the deflection, Fig.1d,c
.To find (Rad.=Rxx) multiply both sides by ‘w’ and integrate over domain.
(∂4w/∂x4 ) = Jxx. Rxx . ………… (2.20 )
Multiply through by ‘w’ and integrate to find, Jxx , for the domain ,
∫∫( ∂4w/∂x4 ) w ∂x ∂y = ∫∫ Jxx Rxx w ∂x∂y (2.21)
For the function given,
Rxx = (m2)(π2) /a2. …………………. (2.22 )
and,
254
6. Innovative Systems Design and Engineering www.iiste.org
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol 2, No 4, 2011
Jxx. =(3/4) m2(π2)/(a2)
Jyy. = (3/4)n2(π2 )/b2)
2.3.1 Twist Transform
From ∂4w/∂x2.∂y2 . = (Jxy) ,
[(m2)(n2)(π2)/(a2.b2)]Cx.Cy . = (Jxy);;(Q4xy.Cx.Cy.=Jxy ) (2.23)
Invoke Eqs.2.7 & 2.8
Kt. =1/4
Coming from, [Cx.Cy]rel,max =2.0 ; [2Cx.Cy. – 2Cx – 2Cy +2]rel,max= 8.0
In this way the twist capacity, w,xxyy, is mixed with, and carried by the tuned values of
‘w,xxxx’ and ‘w,yyyy’. The twist is not independently tuned. So,
∫∫Q4xy. Kt.(2Cx.Cy.-Cx-Cy).w = Jxy.∫∫ w
Jxy = 0.375 Q4xy.
∂4w/∂x2.∂y2. = (Jxy) = (0.375)(m2 .n2) π4/(a2 .b2) .
Solving Equation-1,
D [Jxx(∂2w/∂x2)/w + 2Jxy. + Jyy(∂2w/∂y2)/w ] = q
Amn = (q/D) / [ Jxx Rxx . +2Jxy . + Jyy Ryy ]
= [q/(Dπ4)]/[0.75m4/a4.+0.75m2.n2./a2.b2+0.75n4./b4 ] …… (2.24)
For m=n=2;x=a/2,y=b/2; (wi,)c = wmax= 0.001151 q a4 /D
Adding ,m=2,n=6;m=6,m=n=2;m=2,n=10 ; wc = 0.001243 ;(Ref-1,0.00126;Ref-8,0.001265); ‘w’ tends
to exact because the tuning support moments in clamped plates do not add to central displacements.
2.3.2 Curvatures/Moments:
Fig.1b has so far been treated and only partial curvatures are expected to be available thus far; the
tuning support curvatures ,(Rad wmax)/2 ,must be applied, reversed, as in Fig.1-c for completion. The
effect of clamping makes the effects of any input support-moments negligible; for example zero
central plate displacements.
[(χx)0,1/2]mn,2,2;4,2;2,6;6,2 .=(π2)[-2(4/3462.76)+(-2(16/24370) )+(-2(40/105968))]=-0.0506 .
255
7. Innovative Systems Design and Engineering www.iiste.org
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol 2, No 4, 2011
Taking more terms the exact maximum clamping moment of ‘-0.0513’ (1) will be reached .
[(χx)1/2,1/2]mn,2,2;4,2;2;6;6,2.=(π2)[2(4/3462.76)+(-2(16/24370))+(2(40/105960))]=0.01727
Allowing for poisson’s ratio of ‘0.3’ the central X-moment =0.01727(1+0.3) =0.0225 qa2. More terms
may be tried here to move the ‘0.0225’ towards the exact result of ‘0.0231’(0.0229-Taylor,etal,2002).
3. Application to Plate Buckling
Plate buckling may be studied by the differential equation,
D(w,xxxx + 2w,xx,yy +w,yyyy . ) + Nx..∂2w/∂x2 = 0 (3.1)
L4w + Nx L2w = 0 ……………………. (3.2)
Where Nx. is the axial compressive force in the X-direction only
Examine a simply supported plate; by Eq.2.9,
L4w = Amn (π6 /16)(mn(m2/a2+n2/b2)2 .) ………. (3.3)
We can find (L2w) as
L2w = J2x. (∂2w /∂x2) / w ………. (3.4)
Multiply through by ‘w’ and integrate over plate and we have,
J2x = Amn. (m n π2/16) ………….. (3.5)
and,
Nx. L2w . = Nx .(J2x)(m2.π2/a2) ………………………… (3.6 )
= (Nx)(Amn (m n π2 /16) (m2 π2/a2) .. (3.7)
From Eqs. 3.3-3.7
Nx = (Dπ2/b2 ) (mb/a + n2 a/m b)2. = (C) (f(m,n,b,a))
For minimum -Nx- keep n=1
a=b , N= 4C ; a=2 b , N= 4C for m=2 ; and so on. These are exact, Timoshenko&Kreiger(1)
4. Application to Stiffness Matrix Analysis of Buckling of Bars/Frames.
The main objective of the present transform method was to develop a constant stiffness analysis of
buckling, and this is now briefly explained.
The basic beam stiffness can be stated as: {Flocal .}= [Klocal .]{Vector}local .; (a*=EA/L ;r=EI/L)
256
8. Innovative Systems Design and Engineering www.iiste.org
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol 2, No 4, 2011
! N ! ! -a* 0 0 a* 0 0 ! u1
2 2
! V1 ! ! 0 -12r/L . -6r/L 0 12r/L . -6r/L ! v1
! M1 ! = ! 0 6r/L 4r 0 -6r/L 2r ! θ1 .. (4.1)
2 2
! V2 ! ! 0 12r/L . 6r/L 0 -12r/L . 6r/L ! v2
! M2 ! ! 0 6r/L 2r 0 -6r/L 4r ! θ2
So, find for (N=axial force, M=moment,V=shear-force; member from point-1 to 2
[ Kglobal . ] = [ TT ] [Klocal .] [T .] ,……………… . (4.2)
The acceleration-displacement ratio means relative-bending-moment – displacement ratio at nodal
points. When the ratio becomes point-wise constant then a solution has been found and that ‘ratio’ is
the buckling load.In final implementation the computed bending moments(accelerations) are
interpreted as gravity loads and analysis progresses by successive approximation using only the same
initial elastic stiffness. Convergence is found within five iterations. In the plate analysis demonstrated
above, the ratio , (Rad ), can be seen to be buckling load factors in the X,Y- directions. Eqs.4.1,4.2 lead
to the computer program.The analysis starts by applying a uniform loading but in iterations the
bending moments are the nodal gravity loads.
4.1 Buckling of column pinned at both ends.
The column (AB),Fig-2 is divided into 20 elements and 21-nodes ; the results are found in Table-
1,below after only three iterations. Note that in this case, Table-1 , the relative moments are the actual
moments (columns2 and 3 ) ; ‘mi is the normal nodal slope-deflection moment . As shown in Table-1
for the pin-pin column the result of ‘1.002’ compares with exact,1.0 ; it must be recalled that the
stiffness solution did not assume a sinusoidal variation which, in a manual solution, would have led to
the same correct result. The result confirms that a column buckles into a sine-curve.
4.2 Buckling of Sway Frame with Fixed Bases / Pinned Bases
This is output in Table-2 ;Fig.3a,b, for a beam-column stiffness ratio of 1.0. Many
more results were output in Johnarry(2009). The intention, here, is to demonstrate the power of the
present method; errors are very small(less than one-percent).
257
9. Innovative Systems Design and Engineering www.iiste.org
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol 2, No 4, 2011
Table-3 give results for pinned base portal frame with I beam./Icol .= 100. Any Ib./Ic.-ratio can be analysed
. The high ratio of 100 may be taken as beam of infinite stiffness relative to the adjoining columns ; in
the Table,Pcr/PEuler.= 0.249(Exact,0.25 for infinite value of the stiffness ratio). Fig.3c gives the pinned-
bases frame-diagram.
Conclusion
The acceleration-displacement ratio transforms method, here, has been shown to, more simply, and
exactly, solve the thin plate problem in transverse bending for displacements, bending moments and
buckling. The plate under central point load is solved more exactly in convergent displacements and
bending moments. All solutions are, in the first instance, with respect to curvatures relative to
boundary values; this allows for possible corrections if support tuning moments have any additional
effects. The employment of a constant initial elastic stiffness for buckling by stiffness matrix is most
desirable and the new method of acceleration- displacement ratio transform has been shown to achieve
it; additional applications may be published. Results for bars and portal building frames are
demonstrated for buckling tests. Even for the limited number of discrete elements the results are exact
to within 1.0-percent. Three iterations are, usually, sufficient in the successive approximation analysis.
References
Stephen P.Timoshenko; S.Woinowsky-Krieger,(1959); Theory of plates and shells McGraw-
Hill,Kogakusha Ltd , International Edition .
Wood,R.H. (1974) ;Effective lengths of columns in multi-storey buildings. The Structural
Engineer ,N0.7,Vol.-52
Horne, M.R.(1975) ;An approximate method for calculating the elastic critical loads in multi-
storey plane Frames .The Structural Engineer,Vol.-5,N0.-53
Francois Cheong-Siat-Moi, Erkam Ozer and Le-Wu Lu,(1977); Strength of steel frames under
gravity loads.Journal of the Structural Division,ASCE,Vol.,103,N0.ST6.
Mottram J.T.(2008) ;Stability analysis for pitched portal frames of fibre-reinforced polymer.
Fourth International Conference of FRP Composites in Civil Engineering, Zurich,
Switzerland.
Ngoji Johnarry ,(2009); Structural Analysis Trainer – Civil engineering series -Rootway
Academy services Limited -Publication
258