The stress analysis of a shear wall with matrix displacement method

Ergun, Mustafa,Ates, Sevket Techno-Press 2015 Structural Engineering and Mechanics, An Int'l Jou Vol.53 No.2

Finite element method (FEM) is an effective quantitative method to solve complex engineering problems. The basic idea of FEM for a complex problem is to be able to find a solution by reducing the problem made simple. If mathematical tools are inadequate to obtain precise result, even approximate result, FEM is the only method that can be used for structural analyses. In FEM, the domain is divided into a large number of simple, small and interconnected sub-regions called finite elements. FEM has been used commonly for linear and nonlinear analyses of different types of structures to give us accurate results of plane stress and plane strain problems in civil engineering area. In this paper, FEM is used to investigate stress analysis of a shear wall which is subjected to concentrated loads and fundamental principles of stress analysis of the shear wall are presented by using matrix displacement method in this paper. This study is consisting of two parts. In the first part, the shear wall is discretized with constant strain triangular finite elements and stiffness matrix and load vector which is attained from external effects are calculated for each of finite elements using matrix displacement method. As to second part of the study, finite element analysis of the shear wall is made by ANSYS software program. Results obtained in the second part are presented with tables and graphics, also results of each part is compared with each other, so the performance of the matrix displacement method is demonstrated. The solutions obtained by using the proposed method show excellent agreements with the results of ANSYS. The results show that this method is effective and preferable for the stress analysis of shell structures. Further studies should be carried out to be able to prove the efficiency of the matrix displacement method on the solution of plane stress problems using different types of structures.

Fuzzy finite element method for solving uncertain heat conduction problems

Chakraverty, S.,Nayak, S. Techno-Press 2012 Coupled systems mechanics Vol.1 No.4

In this article we have presented a unique representation for interval arithmetic. The traditional interval arithmetic is transformed into crisp by symbolic parameterization. Then the proposed interval arithmetic is extended for fuzzy numbers and this fuzzy arithmetic is used as a tool for uncertain finite element method. In general, the fuzzy finite element converts the governing differential equations into fuzzy algebraic equations. Fuzzy algebraic equations either give a fuzzy eigenvalue problem or a fuzzy system of linear equations. The proposed methods have been used to solve a test problem namely heat conduction problem along with fuzzy finite element method to see the efficacy and powerfulness of the methodology. As such a coupled set of fuzzy linear equations are obtained. These coupled fuzzy linear equations have been solved by two techniques such as by fuzzy iteration method and fuzzy eigenvalue method. Obtained results are compared and it has seen that the proposed methods are reliable and may be applicable to other heat conduction problems too.

유한체적법에 근거한 단조공정 시뮬레이터를 이용한 난형상 열간단조 공정의 컴퓨터 시뮬레이션

엄재근(Eom J. G),최인수(Choi I. S),김홍태(Kim H. T),이민철(Lee M. C),박성용(Park S. Y),전만수(Joun M. S) 대한기계학회 2006 대한기계학회 춘추학술대회 Vol.2006 No.11

The finite volume method for forging simulation is examined to reveal its possibility as well as its problem in this paper. For this study, the finite volume method based MSC/SuperForge and the finite element method based AFDEX are employed. The simulated results of the homogeneous compression obtained by the two softwares are compared to indicate the problems of the finite volume method while several application examples are given to show the possibility of the finite volume method for simulation of complex hot forging processes. It is shown that the finite volume method can not predict the exact solution of the homogeneous compression especially in terms of forming load and deformed shape but that it is helpful to simulate very complex forging processes which can hardly be simulated by the conventional finite element method.

The stress analysis of a shear wall with matrix displacement method

Mustafa Ergun,Sevket Ates 국제구조공학회 2015 Structural Engineering and Mechanics, An Int'l Jou Vol.53 No.2

Finite element method (FEM) is an effective quantitative method to solve complex engineering problems. The basic idea of FEM for a complex problem is to be able to find a solution by reducing the problem made simple. If mathematical tools are inadequate to obtain precise result, even approximate result, FEM is the only method that can be used for structural analyses. In FEM, the domain is divided into a largenumber of simple, small and interconnected sub-regions called finite elements. FEM has been used commonly for linear and nonlinear analyses of different types of structures to give us accurate results of plane stress and plane strain problems in civil engineering area. In this paper, FEM is used to investigate stress analysis of a shear wall which is subjected to concentrated loads and fundamental principles of stress analysis of the shear wall are presented by using matrix displacement method in this paper. This study is consisting of two parts. In the first part, the shear wall is discretized with constant strain triangular finiteelements and stiffness matrix and load vector which is attained from external effects are calculated for each of finite elements using matrix displacement method. As to second part of the study, finite element analysis of the shear wall is made by ANSYS software program. Results obtained in the second part are presentedwith tables and graphics, also results of each part is compared with each other, so the performance of the matrix displacement method is demonstrated. The solutions obtained by using the proposed method show excellent agreements with the results of ANSYS. The results show that this method is effective and preferable for the stress analysis of shell structures. Further studies should be carried out to be able to prove the efficiency of the matrix displacement method on the solution of plane stress problems using different types of structures.

Finite volumes vs finite elements. There is a choice

Demirdzic, Ismet Techno-Press 2020 Coupled systems mechanics Vol.9 No.1

Despite a widely-held belief that the finite element method is the method for the solution of solid mechanics problems, which has for 30 years dissuaded solid mechanics scientists from paying any attention to the finite volume method, it is argued that finite volume methods can be a viable alternative. It is shown that it is simple to understand and implement, strongly conservative, memory efficient, and directly applicable to nonlinear problems. A number of examples are presented and, when available, comparison with finite element methods is made, showing that finite volume methods can be not only equal to, but outperform finite element methods for many applications.

Polyhedral elements by means of node/edge‐based smoothed finite element method

Lee, Chan,Kim, Hobeom,Im, Seyoung John Wiley Sons, Ltd 2017 International Journal for Numerical Methods in Eng Vol.110 No.11

<P><B>Summary</B></P><P>The node‐based or edge‐based smoothed finite element method is extended to develop polyhedral elements that are allowed to have an arbitrary number of nodes or faces, and so retain a good geometric adaptability. The strain smoothing technique and implicit shape functions based on the linear point interpolation make the element formulation simple and straightforward. The resulting polyhedral elements are free from the excessive zero‐energy modes and yield a robust solution very much insensitive to mesh distortion. Several numerical examples within the framework of linear elasticity demonstrate the accuracy and convergence behavior. The smoothed finite element method‐based polyhedral elements in general yield solutions of better accuracy and faster convergence rate than those of the conventional finite element methods. Copyright © 2016 John Wiley & Sons, Ltd.</P>

Time-varying meshing stiffness calculation of an internal gear pair with small tooth number difference by considering the multi-tooth contact problem

Guangjian Wang,Qing Luo,Shuaidong Zou 대한기계학회 2021 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.35 No.9

Due to the multiple tooth contact problem involving internal gear pair with small tooth number difference (IGPSTND), the existing analytical methods applied for standard spur or helix gear pairs to calculate the time-varying meshing stiffness (TVMS) are not suitable. In this paper, two methods are proposed for calculating the time-varying meshing stiffness in internal gear pairs with small tooth difference. In the first method, an analytical model is established by using the potential energy method, considering the clearance of initial contact tooth and the external load. The second method proposes the application of a hybrid finite elementanalytical method. The proposed two methods are validated by the application of the finite element method. By taking the results of finite element analysis as a comparative reference, the results show that the finite element - analytical method is closer to the reference results than the results obtained by the analytical method, and both methods are less computationally expensive than finite element analysis.

Topology optimization of bounded acoustic problems using the hybrid finite element-wave based method

Goo, S.,Wang, S.,Kook, J.,Koo, K.,Hyun, J. North-Holland Pub. Co 2017 Computer methods in applied mechanics and engineer Vol.313 No.-

This paper presents an alternative topology optimization method for bounded acoustic problems that uses the hybrid finite element-wave based method (FE-WBM). The conventional method for the topology optimization of bounded acoustic problems is based on the finite element method (FEM), which is limited to low frequency applications due to considerable computational efforts. To this end, we propose a gradient-based topology optimization method that uses the hybrid FE-WBM whereby the entire domain of a problem is partitioned into design and non-design domains. In this respect, the FEM is used as a design domain of topology optimization, and the WBM is used as a non-design domain to increase computational efficiency. The adjoint variable method based on the hybrid FE-WBM is also proposed as a means of computing design sensitivities. Numerical examples are presented to demonstrate the effectiveness of the proposed method. We compare the optimized design obtained from the proposed method to that obtained from the conventional method in terms of objective function values, optimized topologies and computational efficiency. The optimization results show that the proposed method can perform more efficient topology optimization than conventional method and can thus be applied to much higher frequency applications that conventional method takes considerable computation time to manage.

An efficient contact algorithm for the interaction of material particles with finite elements

Cheon, Young-Jo,Kim, Hyun-Gyu Elsevier 2018 Computer methods in applied mechanics and engineer Vol.335 No.-

<P><B>Abstract</B></P> <P>In this paper, we propose an efficient contact algorithm to analyze the interaction of material particles with finite elements. The contact forces between material particles and finite elements are computed at the (background) grid nodes in material point method, and transferred to finite element nodes. A weighted average method is used to obtain the velocities at grid nodes contributed from finite element nodes, and a cut-off weight is applied to the contact condition to avoid an early contact occurring in a grid-based contact algorithm. A severe penetration of material particles into finite elements when the finite element mesh is coarser than the background grid can be prevented by introducing distributed interaction (DI) nodes on the contact faces of finite elements. Numerical examples show the effectiveness of the present method to treat the contact interaction between material particles and finite elements.</P>

변형해석을 위한 적응적 세분화방법에 기초한 무요소법

한규택,Han, Kyu-Taek 한국금형공학회 2013 한국금형공학회지 Vol.7 No.1

The finite element method(FEM) presents some limitations when the mesh becomes highly distorted. For analysis of metal forming processes with large deformation, the conventional finite element method usually requires several remeshing operations due to severe mesh distortion. The new computational method developed in the recent years, usually designated by meshfree method, offers an attractive approach to avoid those time-consuming remeshing efforts. This new method uses a set of points to represent the problem domain with no need of an additional mesh. Also this new generation of computational method provides a higher rate of convergence than that of the conventional finite element methods. One of the promising applications of meshfree methods is the adaptive refinement for problems having multi-scale nature. In this study, an adaptive node generation procedure is proposed and also to illustrate the efficiency of proposed method, several numerical examples are presented.