Efficient finite element analysis using graph-theoretical force method; rectangular plane stress and plane strain serendipity family elements

In this paper, the purpose is to present an efficient graph method for the analysis of truss structures using the force method and compare the computational time with that of the stiffness approach. Naturally, the results of the optimization and the accuracy of calculation for both methods are identical, but the calculation time for the force method is less when the degree of static indeterminacy (DSI) is smaller than the degree of kinematic indeterminacy (DKI) of the structure. Three examples are designed, and optimization has been performed using the ECBO algorithm in MATLAB.

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“…Different algorithms are available for optimization with various applications [26,[28][29][30][31][32].…”

Section: Optimization Algorithmsmentioning

confidence: 99%

Optimal Design of Planar Trusses Using Graph Theoretical Force Method

Kaveh

Khavaninzadeh²

2022

Period. Polytech. Civil Eng.

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“…The first class takes the element forces along the edges of the elements [21][22][23][24][25] and in the second class the element forces are concentrated at the mid-edge of the edges of the elements [26,27]. In this paper, an efficient method is developed for the formation of null bases for finite element models comprising of rectangular plane stress and plane strain Lagrange family elements leading to highly sparse and banded flexibility matrices, and can be used for optimal finite element analysis by the force method.…”

Section: Introductionmentioning

confidence: 99%

Efficient finite element analysis using graph-theoretical force method; rectangular plane stress and plane strain Lagrange family elements

Kaveh

Massoudi

2015

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 99%

“…were employed to divide complicated large problems into sub-systems and solve the smaller parts with less computational complexity and then combine the solutions (i.e. divide and conquer methods) [1][2][3][4][5][6][7].There are various structural/mechanical systems with geometries close to those of regular structures, but not satisfying the required mathematical conditions to be considered as regular. A model is called regular if it can be considered as the product of two or three graphs [1].…”

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confidence: 99%

A Numerical Method for Eigensolution of Near-Regular Structural and Mechanical Systems

Shojaei¹,

Kaveh

Rahami³

2016

Period. Polytech. Civil Eng.

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In this paper a numerical method is developed to find the eigenvalues of the Laplacian matrix for near-regular graph models. Considering the similarity between the pattern of the IntroductionAlthough the advent of powerful computers have smoothened the way for the swift computations structural/mechanical systems, the analysis of complicated systems are still laborious and time-consuming. Many algorithms for the solutions of largescale structural/mechanical systems have been developed over the past three decades. These algorithms have mainly aimed to find efficient solutions for the structural governing equations (i.e. F = K∆) and/or eigensolution of a system (i.e. frequencies of free vibration). However, due to the variety of systems and lack of general patterns, most algorithms are limited to partial applications. The most successful advancements were achieved in the solution of symmetric and regular patterns wherein linear algebra, graph products, group theoretical method, U-transformation etc. were employed to divide complicated large problems into sub-systems and solve the smaller parts with less computational complexity and then combine the solutions (i.e. divide and conquer methods) [1][2][3][4][5][6][7].There are various structural/mechanical systems with geometries close to those of regular structures, but not satisfying the required mathematical conditions to be considered as regular. A model is called regular if it can be considered as the product of two or three graphs [1]. A near regular model consists of a regular submodel with limited number of members and/or nodes being added or removed. Recent efforts have been devoted to realize, classify and solve these near-regular patterns efficiently through the available solution of the regular part [8][9][10][11][12]. While several flexibility and stiffness methods, and finite difference and finite element formulations were developed to solve the final governing equation F = K∆, less success were achieved for the eigensolution of the near-regular systems [8][9][10][11][12]. Compared to the solution of F = K∆, eigenvalue problems are more sensitive to the algebraic manipulations. This often leads to matrices with general patterns that cannot usually be solved using specific efficient solvers.In this paper a numerical algorithm is presented for obtaining the eigenvalues of near-regular structures. In this method utilizing the decomposition of block matrices, a determinant equation is obtained. This equation includes separate submatrices corre-

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Efficient finite element analysis using graph-theoretical force method; rectangular plane stress and plane strain serendipity family elements

Cited by 6 publications

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Optimal Design of Planar Trusses Using Graph Theoretical Force Method

Optimal Design of Planar Trusses Using Graph Theoretical Force Method

Efficient finite element analysis using graph-theoretical force method; rectangular plane stress and plane strain Lagrange family elements

A Numerical Method for Eigensolution of Near-Regular Structural and Mechanical Systems

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