Structural Topology Optimization Based on the Smoothed Finite Element Method

Abstract

In this paper, the smoothed finite element method, incorporated with the level set method, is employed to carry out the topology optimization of continuum structures. The structural compliance is minimized subject to a constraint on the weight of material used. The cell-based smoothed finite element method is employed to improve the accuracy and stability of the standard finite element method. Several numerical examples are presented to prove the validity and utility of the proposed method. The obtained results are compared with those obtained by several standard finite elementbased examples in order to access the applicability and effectiveness of the proposed method. The common numerical instabilities of the structural topology optimization problems such as checkerboard pattern and mesh dependency are studied in the examples.

Checkerboard-free topology optimization for compliance minimization of continuum elastic structures based on the generalized finite-volume theory

“…Since Bendsøe and Kikuchi (1988), a significant part of the advances in topology optimization has been obtained through methodologies based on the compliance minimization problem, whose concepts are well-established (Collet et al, 2017). Some examples of applications using this type of optimization problem are presented in Rozvany (2009), Lopes et al (2015), Shobeiri (2016), and Wang et al (2017). Here, it is used the topology optimization problem for compliance minimization, where the design domain is assumed to be rectangular and discretized in rectangular elements or subvolumes.…”

Bidirectional evolutionary structural optimization for nonlinear structures under dynamic loads

“…The level set method was used to vary the structure outline to generate optimal shapes and topologies. 12 The ESO method was proposed based on the gradual elimination of inefficient materials. 10 In this method, the Von Mises stress or strain energy density is calculated for each element and in each step low-stressed elements are removed from the structure.…”

“…Other topology optimization methods have also been proposed and developed. The level set method was used to vary the structure outline to generate optimal shapes and topologies . The ESO method was proposed based on the gradual elimination of inefficient materials .…”

Biomechanical Study of the Development of Long Bones: Finite Element Structure Synthesis of the Human Second Proximal Phalanx Under Growth Conditions

“…Initial and boundary conditions (input) cause spatial mechanical stress distribution influencing resorption and growth of bone, or cause differentiation of mesenchymal stem cells in a homogenous volume (process) and thereby lead to a resulting shape and structure (output) (Lipphaus and Witzel, ). If input and process are known, FESS can be used to obtain resulting morphologies, for example, by predicting preoperatively bone remodeling after implantation or generating a design for optimized lightweight topology in mechanical engineering (Lerch et al, ; Witzel, ; Shobeiri, ). Assumptions of forces causing a specific bone morphology can be tested by using a verified process and comparing the simulation output with real structures.…”