Improvement in 3D topology optimization with h ‐adaptive refinement using the Cartesian grid Finite Element Method

2021 ◽  
Author(s):  
David Muñoz ◽  
José Albelda ◽  
Juan José Ródenas ◽  
Enrique Nadal
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Cartesian Grid ◽  
Adaptive Refinement ◽  
3D Topology ◽  
Element Method

Topology Optimization Using Node-Based Smoothed Finite Element Method

2015 ◽  
Vol 07 (06) ◽  
pp. 1550085 ◽  
Author(s):  
Z. C. He ◽  
G. Y. Zhang ◽  
L. Deng ◽  
Eric Li ◽  
G. R. Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Optimization Design ◽  
Solid Mechanics ◽  
Optimality Criteria ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Smoothed Finite Element Method ◽  
Element Method

The node-based smoothed finite element method (NS-FEM) proposed recently has shown very good properties in solid mechanics, such as providing much better gradient solutions. In this paper, the topology optimization design of the continuum structures under static load is formulated on the basis of NS-FEM. As the node-based smoothing domain is the sub-unit of assembling stiffness matrix in the NS-FEM, the relative density of node-based smoothing domains serves as design variables. In this formulation, the compliance minimization is considered as an objective function, and the topology optimization model is developed using the solid isotropic material with penalization (SIMP) interpolation scheme. The topology optimization problem is then solved by the optimality criteria (OC) method. Finally, the feasibility and efficiency of the proposed method are illustrated with both 2D and 3D examples that are widely used in the topology optimization design.

scholarly journals Optimization of bucket tooth excavator design using topology optimization and finite element method

2021 ◽  
Vol 1858 (1) ◽  
pp. 012081
Author(s):  
Sumar Hadi Suryo ◽  
Rachmat Suryadi Sastra ◽  
Muchammad ◽  
Harto
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Element Method

scholarly journals An interface-enriched generalized finite element method for level set-based topology optimization

2020 ◽  
Vol 63 (1) ◽  
pp. 1-20
Author(s):  
S. J. van den Boom ◽  
J. Zhang ◽  
F. van Keulen ◽  
A. M. Aragón
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Level Set ◽  
Element Formulation ◽  
Generalized Finite Element Method ◽  
Level Set Function ◽  
Analytical Sensitivities ◽  
Generalized Finite Element ◽  
Element Method

AbstractDuring design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e.g., wave propagation or fluid-structure interaction. A level set description of the boundary, when combined with an enriched finite element formulation, offers a smoother description of the design than traditional density-based methods. However, existing enriched methods have drawbacks, including ill-conditioning and difficulties in prescribing essential boundary conditions. In this work, we introduce a new enriched topology optimization methodology that overcomes the aforementioned drawbacks; boundaries are resolved accurately by means of the Interface-enriched Generalized Finite Element Method (IGFEM), coupled to a level set function constructed by radial basis functions. The enriched method used in this new approach to topology optimization has the same level of accuracy in the analysis as the standard finite element method with matching meshes, but without the need for remeshing. We derive the analytical sensitivities and we discuss the behavior of the optimization process in detail. We establish that IGFEM-based level set topology optimization generates correct topologies for well-known compliance minimization problems.

Topology Optimization of Compliant Mechanisms Based on Interpolation Meshless Method and Geometric Nonlinearity

2019 ◽  
Author(s):  
Yonghong Zhang ◽  
Zhenfei Zhao ◽  
Yaqing Zhang ◽  
Wenjie Ge
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Galerkin Method ◽  
Meshless Method ◽  
Geometric Nonlinearity ◽  
Compliant Mechanism ◽  
Linear Convergence ◽  
The Finite Element Method ◽  
Element Method

Abstract In order to prevent mesh distortion problem arising in topology optimization of compliant mechanism with massive displacement, a meshless Galerkin method was proposed and studied in this paper. The element-free Galerkin method (EFG) is more accurate than the finite element method, and it does not need grids. However, it is difficult to impose complex boundaries. This paper presents a topology optimization method based on interpolation meshless method, which retains the advantages of the finite element method (FEM) that is easy to impose boundary conditions and high accuracy of the meshless method. At the same time, a method of gradually reducing step is proposed to solve the problem of non-linear convergence caused by low-density points in topology optimization. Numerical example shows that these techniques are valid in topology optimization of compliant mechanism considering the geometric nonlinearity, and simultaneously these techniques can also improve the convergence of nonlinearity.

scholarly journals Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method

2016 ◽  
Vol 472 (2189) ◽  
pp. 20150835 ◽  
Author(s):  
Yongbo Deng ◽  
Jan G. Korvink
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Electromagnetic Waves ◽  
Three Dimensional ◽  
Free Condition ◽  
Edge Element ◽  
Divergence Free ◽  
The Magnetic Field ◽  
Element Method

This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.

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