scholarly journals Topology optimization with incompressible materials under small and finite deformations using mixed u/p elements

2018 ◽  
Vol 115 (8) ◽  
pp. 1015-1052 ◽  
Author(s):  
Guodong Zhang ◽  
Ryan Alberdi ◽  
Kapil Khandelwal
Keyword(s):  
Topology Optimization ◽  
Finite Deformations ◽  
P Elements ◽  
Incompressible Materials

Topology Optimization Algorithm for Plates and Shells Subjected to Plastic Deformations

1998 ◽  
Author(s):  
Kohei Yuge ◽  
Nobuhiro Iwai ◽  
Noboru Kikuchi
Keyword(s):  
Topology Optimization ◽  
Optimization Method ◽  
Homogenization Method ◽  
Finite Deformations ◽  
Thin Shells ◽  
Plastic Deformations ◽  
Material Tensor ◽  
Design Variables ◽  
Interpolation Technique ◽  
Plates And Shells

Abstract A topology optimization method for plates and shells subjected to plastic deformations is presented. The algorithms is based on the generalized layout optimization method invented by Bendsϕe and Kikuchi (1988), where an admissible design domain is assumed to be composed of microstructures with periodic cavities. The sizes of the cavities and the rotational angles of the microstructures are design variables which are optimized so as to minimize the applied work. The macroscopic material tensor for the porous material is numerically calculated by the homogenization method for the sensitivity analysis. In this paper, the method is applied to two-dimensional elasto-plastic problems. A database of the material tensor and its interpolation technique are presented. The algorithm is expanded into thin shells subjected to finite deformations. Several numerical examples are shown to demonstrate the effectiveness of these algorithms.

Stress Analysis for a Nonlinear Viscoelastic Compressible Cylinder

1970 ◽  
Vol 37 (4) ◽  
pp. 1127-1133 ◽  
Author(s):  
E. C. Ting
Keyword(s):  
Large Deformations ◽  
Finite Deformations ◽  
Kernel Functions ◽  
Nonlinear Viscoelastic ◽  
Stress Strain Relation ◽  
Incompressible Materials ◽  
Small Deformations ◽  
Compressible Cylinder ◽  
Elastic Casing ◽  
Finite Difference Techniques

Real solids are not incompressible, although many viscoelastic materials which undergo large deformations show only small changes in volume under ordinary loading conditions. This paper is concerned with a pressurized isotropic viscoelastic hollow cylinder bonded to an elastic casing in which, during a finite deformation, the dilatational change in any element of the cylinder is a small quantity. The analysis is based in part upon the theory of small deformations superposed on finite deformations. Numerical calculations are evaluated by using finite-difference techniques and assuming particular forms of kernel functions in the stress-strain relation. The results for compressible and incompressible materials are compared.

scholarly journals Mixed/Hybrid finite elements for finite deformations of quasi‐incompressible materials with non‐constant bulk moduli

PAMM ◽  
2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Patrick Schneider ◽  
Josef Arthur Schönherr ◽  
Christian Mittelstedt
Keyword(s):  
Finite Elements ◽  
Finite Deformations ◽  
Incompressible Materials

Topology optimization of tension-only cable nets under finite deformations

2020 ◽  
Vol 62 (2) ◽  
pp. 559-579
Author(s):  
Emily D. Sanders ◽  
Adeildo S. Ramos ◽  
Glaucio H. Paulino
Keyword(s):  
Topology Optimization ◽  
Finite Deformations ◽  
Cable Nets
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