scholarly journals Prestress Design of Tensegrity Structures Using Semidefinite Programming

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Yafeng Wang ◽  
Xian Xu
Keyword(s):  
Semidefinite Programming ◽  
Stiffness Matrix ◽  
Global Optimality ◽  
Stability Criteria ◽  
Minimum Eigenvalue ◽  
Tensegrity Structures ◽  
Tangent Stiffness Matrix ◽  
Deterministic Algorithms ◽  
Semidefinite Programming Problem ◽  
Internal Forces

Finding appropriate prestresses which can stabilize the system is a key step in the design of tensegrity structures. A semidefinite programming- (SDP-) based approach is developed in this paper to determine appropriate prestresses for tensegrity structures. Three different stability criteria of tensegrity structures are considered in the proposed approach. Besides, the unilateral property of members and the evenness of internal forces are taken into account. The stiffness of the whole system can also be optimized by maximizing the minimum eigenvalue of the tangent stiffness matrix. Deterministic algorithms are used to solve the semidefinite programming problem in polynomial time. The applicability of the proposed approach is verified by three typical examples. Compared to previous stochastic-based approaches, the global optimality of the solution of the proposed approach is theoretically guaranteed and the solution is exactly reproducible.

scholarly journals ANÁLISE NÃO-LINEAR DE ARCOS UTILIZANDO O ELEMENTO DE VIGA UNIFICADO BERNOULLI-TIMOSHENKO E A FORMULAÇÃO CO-ROTACIONAL

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Gabriel Costa Oliveira ◽  
William Taylor Matias Silva
Keyword(s):  
Rigid Body ◽  
Stiffness Matrix ◽  
Deformation Modulus ◽  
Shear Locking ◽  
Pure Bending ◽  
Tangent Stiffness Matrix ◽  
Natural Modes ◽  
Material Stiffness ◽  
Internal Forces ◽  
Body Components

RESUMO: Neste trabalho é descrita a formulação co-rotacional de um elemento de viga unificado, que engloba as teorias de Euler-Bernoulli e de Timoshenko e que não apresenta bloqueio por cisalhamento. A cinemática co-rotacional se baseia na separação do movimento de um sólido em uma parte deformacional, e a outra, em movimento de corpo rígido. O movimento deformacional do elemento é descrito por três modos naturais de deformação relacionados aos esforços axial, de flexão pura e de flexão simples, respectivamente. Os esforços internos gerados pelos modos de deformação naturais são autoequilibrados, o que permite obter uma matriz de rigidez tangente consistente. Descreve-se de forma detalhada a obtenção das matrizes de rigidez geométrica e material. Por meio de alguns exemplos numéricos é demonstrada a habilidade do elemento de viga unificado em lidar com grandes translações e rotações de corpo-rígido.
 
 ABSTRACT: This present paper describes the co-rotational formulation for unified beams, that combine the Euler-Bernoulli and the Timoshenko theories, witch don’t have problems with shear locking. The co-rotational cinematic is based on the separation of the montion in deformational and rigid body components. The deformation movement of the element is described by three natural modes of deformation related to the axial efforts, pure bending and simple bending. The internal forces generated by the natural deformation modulus are self-equilibrated which allows to obtain a consistent tangent stiffness matrix. Development of the geometric and the material stiffness matrix is described in details. Throughout some numerical examples present the ability of the co-rotational formulation for unified beams to handle with large translations and rotations of rigid body.

DESIGN OF LATERAL BRACES FOR COLUMNS CONSIDERING CRITICAL IMPERFECTION OF BUCKLING

2004 ◽  
Vol 04 (01) ◽  
pp. 69-88 ◽  
Author(s):  
J. TAKAGI ◽  
M. OHSAKI
Keyword(s):  
Stiffness Matrix ◽  
Load Condition ◽  
Buckling Modes ◽  
Tangent Stiffness ◽  
Tangent Stiffness Matrix ◽  
Total Potential ◽  
Column Type ◽  
Global Buckling ◽  
Imperfect System ◽  
Allowable Stress Design

The present paper discusses the design of column-type structures, which are composed of columns and lateral braces attached perpendicular to the columns. Buckling of the braces of this kind of structures directly leads to global buckling of the columns. The brace-buckling modes are successfully detected by considering higher-order geometrically nonlinear relations and by introducing Green's strain into the total potential energy of the structure. Sensitivity analysis of the eigenvalues of the tangent stiffness matrix under fixed load condition is carried out with respect to imperfections of the nodal locations. Furthermore, the critical imperfection that most drastically reduces the eigenvalues are calculated and buckling loads of the imperfect systems are evaluated. The numerical results show that the second or higher eigenmode of the tangent stiffness matrix of the perfect system should be sometimes used for estimating the buckling load of the imperfect system. Design examples are presented using the proposed method, and they are compared with those in accordance with an allowable-stress design standard. The results show a possibility of reducing the sizes of the brace sections.

Development of Bifurcation Analysis Method for Rate Dependent Materials

2019 ◽  
Vol 794 ◽  
pp. 220-225
Author(s):  
Daiki Towata ◽  
Yuichi Tadano
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Bifurcation Analysis ◽  
Stiffness Matrix ◽  
Computational Method ◽  
Analysis Method ◽  
The Finite Element Method ◽  
Tangent Stiffness Matrix ◽  
Rate Dependent ◽  
Element Method

In this study, a novel numerical method to analyze the bifurcation problemof a rate dependent material using the finite element method is proposed. The consistent stiffness matrix, which is required for a bifurcation analysis using the finite element method, for a rate dependent material is generally hard to compute, therefore, a computational method to calculate the tangent stiffness matrix based on a numerical differential is introduced so that exact bifurcation analyses for the rate dependent material can be conducted. A numerical example of the proposed method is demonstrated, and the adequacy of the proposed method is discussed.

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