Element deformation scaling for robust geometrically nonlinear analyses in topology optimization

Dijk, Nico P. van; Langelaar, Matthijs; Keulen, Fred van

doi:10.1007/s00158-014-1145-4

Cited by 29 publications

(14 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is widely accepted that the excessive distortion of low densities elements in density-based topology optimization of geometrically nonlinear structures leads to the failure of FEA in topology optimization. [24][25][26]47 The energy interpolation equation, 30 which models the low density elements in linear theory rather than nonlinear theory, is employed to surmount the numerical instability resulting from the low density elements. The equation is effective to avoid the vibration of the low density elements.…”

Section: Discussionmentioning

confidence: 99%

“…The difference between n c is used to evaluate the effect of the modifications in alleviating the numerical difficulties. 25 The difference between the contractile displacementsū of the solutions to the original model 11 and the modified model is used to evaluate the reasonability of these modifications.…”

Section: Examples With and Without The Stabilization Methodsmentioning

confidence: 99%

“…Many methods have been proposed to address this difficulty. These methods include element connectivity scaling, 24 element deformation scaling, 25 modified constitutive models, 26 the Levenberg-Marquardt method, 27 the equivalent static load method, 28 the moving isosurface threshold method, 29 and the energy interpolation scheme. 30 All of them are found to be effective when the materials are deformed passively.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Topology optimization of fusiform muscles with a maximum contraction

Chen

Zhang

Zhu

2018

Numer Methods Biomed Eng

View full text Add to dashboard Cite

Understanding the optimal designs in nature is critical in bionics. This paper presents a method for designing the configuration of fusiform muscle with a maximum contractile displacement based on topology optimization methods. A nearly incompressible continuum constitutive model of skeletal muscle is utilized. The contractile displacement from the relaxed state to the contracted state is regarded as the objective function. To handle the numerical difficulties that result from the existence of element density, an energy interpolation equation is employed, and a modification of the constitutive model of skeletal muscle is proposed. Several numerical examples are given to demonstrate the reasonability of the proposed method.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Examples With and Without The Stabilization Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Topology optimization of fusiform muscles with a maximum contraction

Chen

Zhang

Zhu

2018

Numer Methods Biomed Eng

View full text Add to dashboard Cite

show abstract

“…To compare the three topologies obtained from different values, additional 300 optimization iterations were carried out for the three cases of the E-interpolation scheme, where the projection scheme in Equation (29) was applied and the results are shown in Figure 16. It can be seen that the objective function values in case-1 ( = 0.4) and case-3 ( = 0.6) are similar, even though the topologies are significantly different.…”

Section: Pressure-loaded Blockmentioning

confidence: 99%

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

Zhang

Alberdi

Khandelwal

2018

Numerical Meth Engineering

View full text Add to dashboard Cite

Summary This paper focuses on topology optimization utilizing incompressible materials under both small‐ and finite‐deformation kinematics. To avoid the volumetric locking that accompanies incompressibility, linear and nonlinear mixed displacement/pressure (u/p) elements are utilized. A number of material interpolation schemes are compared, and a new scheme interpolating both Young's modulus and Poisson's ratio (E‐ν interpolation) is proposed. The efficacy of this proposed scheme is demonstrated on a number of examples under both small‐ and finite‐deformation kinematics. Excessive mesh distortions that may occur under finite deformations are dealt with by extending a linear energy interpolation approach to the nonlinear u/p formulation and utilizing an adaptive update strategy. The proposed optimization framework is demonstrated to be effective through a number of representative examples.

show abstract

“…proposed a new interpolation scheme in which the strain energy density (SED) of low-density elements and high-density elements was modelled using small deformation theory and large deformation theory, respectively. An element deformation scaling approach was used by van Dijk, Langelaar, and van Keulen (2014) to scale the local internal displacements in low-density elements. Xie (2007, 2008) suggested using hard-kill BESO to increase the computational efficiency and avoid issues regarding the existence of intermediate-density elements.…”

Section: Introductionmentioning

confidence: 99%

Topology optimization of geometrically nonlinear structures using an evolutionary optimization method

Abdi

Ashcroft

Wildman

2018

Engineering Optimization

View full text Add to dashboard Cite

A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. ABSTRACTThe topology optimization using isolines/isosurfaces and extended finite element method (Iso-XFEM) is an evolutionary optimization method developed in previous studies to enable the generation of high-resolution topology optimized designs suitable for additive manufacture. Conventional approaches for topology optimization require additional postprocessing after optimization to generate a manufacturable topology with clearly defined smooth boundaries. Iso-XFEM aims to eliminate this timeconsuming post-processing stage by defining the boundaries using isovalues of a structural performance criterion and an extended finite element method (XFEM) scheme. In this article, the Iso-XFEM method is further developed to enable the topology optimization of geometrically nonlinear structures undergoing large deformations. This is achieved by implementing a total Lagrangian finite element formulation and defining a structural performance criterion appropriate for the objective function of the optimization problem. The Iso-XFEM solutions for geometrically nonlinear test cases implementing linear and nonlinear modelling are compared, and the suitability of nonlinear modelling for the topology optimization of geometrically nonlinear structures is investigated. ARTICLE HISTORY

show abstract

Element deformation scaling for robust geometrically nonlinear analyses in topology optimization

Cited by 29 publications

References 28 publications

Topology optimization of fusiform muscles with a maximum contraction

Topology optimization of fusiform muscles with a maximum contraction

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

Topology optimization of geometrically nonlinear structures using an evolutionary optimization method

Contact Info

Product

Resources

About