Mixed analysis of shell and solid elements using the overlaying mesh method

Nakasumi, Shogo; Suzuki, Katsuyuki; Fujii, Daiji; Ohtsubo, Hideomi

doi:10.1007/s007730300009

Cited by 9 publications

(7 citation statements)

References 4 publications

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“…It can be seen that the implicit boundary of the initial design shown in Figure 15 can be developed and broken apart (Figures 18(a)-(c)) and merged together (Figures 18(d)-(f)), due to the use of the powerful level set method, as discussed in detail in Reference [18]. Smooth and stable propagation of the implicit boundary has also been experienced due to the linear filter shown in Equation (35) for the normal velocity around the front to smooth the discontinuity. As a comparison, Figure 19 shows the evolution history of the final design without using the smoothing linear filter.…”

Section: Michell Type Structurementioning

confidence: 89%

“…To build a local FE mesh, the linear triangular element, rather than the 2D quadrilateral element in Reference [38] or 3D element in References [33][34][35], is adopted in the present study because of its flexibility to deal with complex geometries [42,43]. Figure 3 displays the local FE mesh region for each segment of the implicit boundary consisting of piecewise lines, in which the elements in the solid and void domains are denoted by solid and dashed lines, respectively.…”

Section: Analysis Model Of the Dynamic Implicit Boundary-based Movingmentioning

confidence: 99%

“…Although attractive in general, this method requires development of special superimposed mesh [39]. The local mesh with 3D elements in References [33][34][35] or overlapping 2D elements in Reference [38] may become too cumbersome and less efficient for structural topology optimization since many moving holes (boundaries) may be involved. Furthermore, ambiguity in the numerical integration in overlaying domains may be produced because of the existence of many discontinuities [36].…”

Section: Introductionmentioning

confidence: 99%

“…The S-FEM was developed to compute the stress distributions of heterogeneous material with special care to study the heterogeneity in Reference [34]. In Reference [35], the S-FEM was applied to the analysis of plate and shell structure problems by superimposing solid elements on plate/shell elements. More recently, Lee et al [36] combined the S-FEM with the X-FEM for modelling of stationary and growing cracks.…”

Section: Introductionmentioning

confidence: 99%

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A moving superimposed finite element method for structural topology optimization

Wang

2006

Int. J. Numer. Meth. Engng

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SUMMARYLevel set methods are becoming an attractive design tool in shape and topology optimization for obtaining efficient and lighter structures. In this paper, a dynamic implicit boundary-based moving superimposed finite element method (s-version FEM or S-FEM) is developed for structural topology optimization using the level set methods, in which the variational interior and exterior boundaries are represented by the zero level set. Both a global mesh and an overlaying local mesh are integrated into the moving S-FEM analysis model. A relatively coarse fixed Eulerian mesh consisting of bilinear rectangular elements is used as a global mesh. The local mesh consisting of flexible linear triangular elements is constructed to match the dynamic implicit boundary captured from nodal values of the implicit level set function. In numerical integration using the Gauss quadrature rule, the practical difficulty due to the discontinuities is overcome by the coincidence of the global and local meshes. A double mapping technique is developed to perform the numerical integration for the global and coupling matrices of the overlapped elements with two different co-ordinate systems. An element killing strategy is presented to reduce the total number of degrees of freedom to improve the computational efficiency. A simple constraint handling approach is proposed to perform minimum compliance design with a volume constraint. A physically meaningful and numerically efficient velocity extension method is developed to avoid the complicated PDE solving procedure. The proposed moving S-FEM is applied to structural topology optimization using the level set methods as an effective tool for the numerical analysis of the linear elasticity topology optimization problems. For the classical elasticity problems in the literature, the present S-FEM can achieve numerical results in good agreement with those from the theoretical solutions and/or numerical results from the standard FEM. For the minimum compliance topology optimization problems in structural optimization, the present approach significantly outperforms the well-recognized 'ersatz material' approach as expected in the accuracy of the strain field, numerical stability, and representation fidelity at the expense of increased computational time. It is also shown that the present approach is able to produce structures near the theoretical optimum. It is suggested that the present S-FEM can be a promising tool for shape and topology optimization using the level set methods.

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Section: Michell Type Structurementioning

confidence: 89%

Section: Analysis Model Of the Dynamic Implicit Boundary-based Movingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A moving superimposed finite element method for structural topology optimization

Wang

2006

Int. J. Numer. Meth. Engng

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“…1, 2009 method was then adopted by many researchers. Nakasumi et al (11) applied the s-FEM to perform the global-local analyses on ship-structures. Okada et al (12) performed two-dimensional fracture mechanics analyses and the accuracy of s-FEM was critically discussed.…”

Section: Journal Of Computational Science and Technologymentioning

confidence: 99%

On the Linear Dependencies of Interpolation Functions in s-Version Finite Element Method

Ooya

Tanaka

Okada

2009

JCST

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In this paper, we first point out that the finite element interpolation functions sometime lose their linear independencies when the elements are superposed each other in s-Version finite element (s-FEM) analyses. This problem has been known among engineers/researchers who have studied and used the s-FEM for solid mechanics analyses. Once the interpolation functions lose their linear independencies, resulting global stiffness matrix becomes singular and, therefore, the solutions lose their uniqueness. Although it is rare for an analyst to come across such a problem, it degrades the robustness of s-FEM. This paper describes a way to judge the occurrence of such a problem and propose a method to circumvent it.

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A crack propagation simulation for a steel CHS T-joint employing an advanced shell-solid finite element modeling

et al. 2021

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Mixed analysis of shell and solid elements using the overlaying mesh method

Cited by 9 publications

References 4 publications

A moving superimposed finite element method for structural topology optimization

A moving superimposed finite element method for structural topology optimization

On the Linear Dependencies of Interpolation Functions in s-Version Finite Element Method

A crack propagation simulation for a steel CHS T-joint employing an advanced shell-solid finite element modeling

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