Topology optimization of geometrically nonlinear structures and compliant mechanisms

1998 ◽  
Author(s):  
Tyler Bruns ◽  
Daniel Tortorelli
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Geometrically Nonlinear ◽  
Nonlinear Structures

scholarly journals Shape preserving design of geometrically nonlinear structures using topology optimization

2019 ◽  
Vol 59 (4) ◽  
pp. 1033-1051 ◽  
Author(s):  
Yu Li ◽  
Jihong Zhu ◽  
Fengwen Wang ◽  
Weihong Zhang ◽  
Ole Sigmund
Keyword(s):  
Topology Optimization ◽  
Geometrically Nonlinear ◽  
Nonlinear Structures ◽  
Shape Preserving

scholarly journals Stiffness optimization of geometrically nonlinear structures and the level set based solution

2016 ◽  
Vol 7 ◽  
pp. A3 ◽  
Author(s):  
Qi Xia ◽  
Tielin Shi
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Optimization Problem ◽  
Two Dimensions ◽  
Geometrically Nonlinear ◽  
Nonlinear Structures ◽  
Element Analysis ◽  
Topology Optimization Problem ◽  
Stiffness Optimization ◽  
Ks Function

Load-normalized strain energy increments between consecutive load steps are aggregated through the Kreisselmeier-Steinhauser (KS) function, and the KS function is proposed as a stiffness criterion of geometrically nonlinear structures. A topology optimization problem is defined to minimize the KS function together with the perimeter of structure and a volume constraint. The finite element analysis is done by remeshing, and artificial weak material is not used. The topology optimization problem is solved by using the level set method. Several numerical examples in two dimensions are provided. Other criteria of stiffness, i.e., the end compliance and the complementary work, are compared.

Multiobjective Topology Optimization of Compliant Microgripper With Geometrically Nonlinearity

2007 ◽  
Author(s):  
Zhaokun Li ◽  
Xianmin Zhang
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Structural Response ◽  
Decision Function ◽  
Element Formulation ◽  
Geometrically Nonlinear ◽  
Conflicting Objectives ◽  
Incremental Scheme ◽  
Moving Asymptotes

Since compliant mechanism is usually required to perform in more than one environment, the ability to consider multiple objectives has to be included within the framework of topology optimization. And the topology optimization of micro-compliant mechanisms is actually a geometrically nonlinear problem. This paper deals with multiobjective topology optimization of micro-compliant mechanisms undergoing large deformation. The objective function is defined by the minimum compliance and maximum geometric advantage to design a mechanism which meets both stiffness and flexibility requirements. The weighted sum of conflicting objectives resulting from the norm method is used to generate the optimal compromise solutions, and the decision function is set to select the preferred solution. Geometrically nonlinear structural response is calculated using a Total-Lagrange finite element formulation and the equilibrium is found using an incremental scheme combined with Newton-Raphson iterations. The solid isotropic material with penalization approach is used in design of compliant mechanisms. The sensitivities of the objective functions are found with the adjoint method and the optimization problem is solved using the Method of Moving Asymptotes. These methods are further investigated and realized with the numerical example of compliant microgripper, which is simulated to show the availability of this approach proposed in this paper.

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