Finite Element Analysis for Engineers

Rieg, Frank; Hackenschmidt, Reinhard; Alber-Laukant, Bettina

doi:10.3139/9781569904886

Cited by 5 publications

(18 citation statements)

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“…Another problem with reducing the size of the finite element mesh is that the optimizer may not have the necessary freedom to find optimum structures and create fine structures where they actually are required. Finally, a coarse mesh may lead to inaccurate results of the FEA and therefore to wrong optimization results [9,10]. This article shows different methods for speeding up the topology optimization by exploiting characteristic features of optimization problems.…”

Section: Startmentioning

confidence: 99%

Methods for Increased Efficiency of FEM-Based Topology Optimization

Glamsch¹,

Deese²,

Rieg³

2019

Int. j. simul. model.

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Lightweight construction is playing an increasingly important role for a wide variety of reasons, such as improving energy efficiency. In addition to lightweight material construction, lightweight structure construction is gaining more and more influence, which is made possible due to topology optimization. The aim of topology optimization is to develop an optimal design proposal based on a construction space model and given boundary conditions (e.g. mechanical or thermal). The calculation of the structural response is often done using the time consuming finite element method (FEM). Since topology optimization is an iterative process, usually many finite element analyses (FEA) have to be performed, which results in high computing time. Therefore, this article presents different methods to minimize computing time by exploiting various special features that occur with FEA in the context of optimizations.

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Section: Startmentioning

confidence: 99%

Methods for Increased Efficiency of FEM-Based Topology Optimization

Glamsch¹,

Deese²,

Rieg³

2019

Int. j. simul. model.

View full text Add to dashboard Cite

show abstract

“…(3), a volume integral must be solved for the calculation of the gravitational nodal forces. If the element formulation is assumed to be isoparametric, the integration can be performed in the natural coordinate system [3]:…”

Section: Element Description and Numerical Integrationmentioning

confidence: 99%

“…(7), is usually carried out by numerical integration [3]. Typically, Gaussian quadrature is used in this context [1], which is based on the idea of evaluating the integrand at certain grid points, so-called Gauss points, and calculating the weighted sum [3]:…”

Section: Element Description and Numerical Integrationmentioning

confidence: 99%

“…The parameters (α a , α b , α c ) denote the Gaussian weights, and (r a , s b , t c ) are the natural coordinates of the Gauss points [3]. These parameters might be different for various element geometries.…”

Section: Element Description and Numerical Integrationmentioning

confidence: 99%

“…The main idea of the FEA is to partition a continuum into a finite number of finitely large subcontinua [1] to [3]. Such discretized elements are referred to as finite elements (FE).…”

Section: Introductionmentioning

confidence: 99%

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