Topology optimization using non-conforming finite elements: three-dimensional case

2005 ◽  
Vol 63 (6) ◽  
pp. 859-875 ◽  
Author(s):  
Gang-Won Jang ◽  
Sangkeun Lee ◽  
Yoon Young Kim ◽  
Dongwoo Sheen
Keyword(s):  
Topology Optimization ◽  
Finite Elements ◽  
Three Dimensional ◽  
Dimensional Case

scholarly journals Solving the hourglass instability problem using rare mesh variation-difference schemes

2021 ◽  
Vol 2099 (1) ◽  
pp. 012003
Author(s):  
D T Chekmarev ◽  
Ya A Dawwas
Keyword(s):  
Finite Elements ◽  
High Efficiency ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Explicit Difference Scheme ◽  
Slow Convergence ◽  
Instability Problem ◽  
Instability Effect ◽  
2D And 3D

Abstract The hourglass instability effect is characteristic of the Wilkins explicit difference scheme or similar schemes based on two-dimensional 4-node or three-dimensional 8-node finite elements with one integration point in the element. The hourglass effect is absent in schemes with cells in the form of simplexes (triangles in two-dimensional case, tetrahedrons in three-dimensional case). But they have another well-known drawback - slow convergence. One of the authors proposed a rare mesh scheme, in which elements in the form of a tetrahedron are located one at a time in the centers of the cells of a hexahedral grid. This scheme showed the absence “hourglass” effect and other drawbacks with high efficiency. This approach was further developed for solving 2D and 3D problems.

An Evolutionary Multi-Objective Optimization Approach to the Topology Optimization of Auxetic Structures

2002 ◽  
Author(s):  
Ashraf O. Nassef
Keyword(s):  
Topology Optimization ◽  
Elastic Modulus ◽  
Finite Elements ◽  
Multiobjective Optimization ◽  
Poisson Ratio ◽  
Optimization Approach ◽  
Multi Objective Optimization ◽  
Finite Elements Analysis ◽  
Multi Objective ◽  
Auxetic Structures

Auxetic structures are ones, which exhibit an in-plane negative Poisson ratio behavior. Such structures can be obtained by specially designed honeycombs or by specially designed composites. The design of such honeycombs and composites has been tackled using a combination of optimization and finite elements analysis. Since, there is a tradeoff between the Poisson ratio of such structures and their elastic modulus, it might not be possible to attain a desired value for both properties simultaneously. The presented work approaches the problem using evolutionary multiobjective optimization to produce several designs rather than one. The algorithm provides the designs that lie on the tradeoff frontier between both properties.

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