Design for Energy Absorption: A Topology Optimization Approach

2001 ◽  
Author(s):  
Hae Chang Gea ◽  
Jianhui Luo
Keyword(s):  
Topology Optimization ◽  
Energy Absorption ◽  
Strain Energy ◽  
Adjoint Method ◽  
Structural Integrity ◽  
Optimization Approach ◽  
Regional Strain ◽  
Vehicle Structure ◽  
Mean Compliance ◽  
Energy Formulation

Abstract Topology optimization for energy absorption is studied in this paper. Unlike conventional mean compliance formulation, this paper considers two main functions of vehicle structure: stiffness and energy absorption. During its normal usages, stiffness is chosen as the design objective. During impact, portion of vehicle structures absorbs impact energy while other part maintains the structural integrity. Therefore, we implemented a regional strain energy formulation to topology optimization. Sensitivity for regional strain energy is derived from the adjoint method. Numerical results from the proposed formulation are presented.

Application of Regional Strain Energy in Topology Optimization With Inertia Relief Analysis

2013 ◽  
Author(s):  
Wei Song ◽  
Hae Chang Gea ◽  
Ren-Jye Yang ◽  
Ching-Hung Chuang
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Strain Energy ◽  
Computational Cost ◽  
Structure Design ◽  
Protective Structure ◽  
Element Analysis ◽  
Regional Strain ◽  
Unbalanced Loads ◽  
Energy Formulation

In finite element analysis, inertia relief solves the response of an unconstrained structure subject to constant or slowly varying external loads with static analysis computational cost. It is very attractive to utilize it in topology optimization to design structures under unbalanced loads, such as in impact and drop phenomena. In this paper, regional strain energy formulation and inertia relief is integrated into topology optimization to design protective structure under unbalanced loads. For background, the equations of inertia relief are introduced and a commonly used solving method is revisited. Then the regional strain energy formulation for topology optimization with inertia relief is proposed and its sensitivity is derived from the adjoint method. Based on the solving method, the sensitivity is evaluated term by term to simplify the results. The simplified sensitivity can be calculated easily using the output of commercial finite element packages. Finally, the effectiveness of this formulation is shown in the first example and the proposed regional strain energy formulation for topology optimization with inertia relief are presented and discussed in the protective structure design examples.

Design of Energy Absorbing Structure Using Topology Optimization With a Multi-Material Model

2003 ◽  
Author(s):  
Daeyoon Jung ◽  
Hae Chang Gea
Keyword(s):  
Topology Optimization ◽  
Strain Energy ◽  
Effective Properties ◽  
Service Condition ◽  
Material Model ◽  
Three Phase ◽  
The Mean ◽  
Energy Absorbing ◽  
Dual Objectives ◽  
Mean Compliance

To accommodate the dual objectives of many engineering applications, one to minimize the mean compliance for the stiffest structure under normal service condition and the other to maximize the strain energy for energy absorption during excessive loadings, topology optimization with a multi-material model is applied to the design of energy absorbing structure in this paper. The effective properties of the three-phase material are derived using a spherical micro-inclusion model. The dual objectives are combined in a ratio formation. Numerical examples from the proposed method are presented and discussed.

scholarly journals Structural Sizing and Topology Optimization Based on Weight Minimization of a Variable Tapered Span-Morphing Wing for Aerodynamic Performance Improvements

Biomimetics ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 55
Author(s):  
Mohamed Elelwi ◽  
Ruxandra Mihaela Botez ◽  
Thien-My Dao
Keyword(s):  
Topology Optimization ◽  
Structural Integrity ◽  
Minimum Weight ◽  
Maximum Speed ◽  
Aerodynamic Load ◽  
Optimization Approach ◽  
Morphing Wing ◽  
Aerodynamic Optimization ◽  
And Topology ◽  
Variable Span

This article proposes the integration of structural sizing, topology, and aerodynamic optimization for a morphing variable span of tapered wing (MVSTW) with the aim to minimize its weight. In order to evaluate the feasibility of the morphing wing optimization, this work creates a numerical environment by incorporating simultaneous structural sizing and topology optimization based on its aerodynamic analysis. This novel approach is proposed for an MVSTW. A problem-specific optimization approach to determine the minimum weight structure of the wing components for its fixed and moving segments is firstly presented. The optimization was performed using the OptiStruct solver inside HyperMesh. This investigation seeks to minimize total structure compliance while maximizing stiffness in order to satisfy the structural integrity requirements of the MVSTW. The aerodynamic load distribution along the wingspan at full wingspan extension and maximum speed were considered in the optimization processes. The wing components were optimized for size and topology, and all of them were built from aluminum alloy 2024-T3. The optimization results show that weight savings of up to 51.2% and 55.7% were obtained for fixed and moving wing segments, respectively. Based on these results, the optimized variable-span morphing wing can perform certain flight missions perfectly without experiencing any mechanical failures.

scholarly journals NODAL COSINE SINE MATERIAL INTERPOLATION IN MULTI OBJECTIVE TOPOLOGY OPTIMIZATION WITH THE GLOBAL CRITERIA METHOD FOR LINEAR ELASTO STATIC, HEAT TRANSFER, POTENTIAL FLOW AND BINARY CROSS ENTROPY SHARPENING

2021 ◽  
Vol 1 ◽  
pp. 2247-2256
Author(s):  
Martin Denk ◽  
Klemens Rother ◽  
Mario Zinßer ◽  
Christoph Petroll ◽  
Kristin Paetzold
Keyword(s):  
Heat Transfer ◽  
Topology Optimization ◽  
Potential Flow ◽  
Cross Entropy ◽  
Objective Criterion ◽  
Multi Objective ◽  
Material Interpolation ◽  
Continuous Material ◽  
Mean Compliance ◽  
Transfer Potential

AbstractTopology optimization is typically used for suitable design suggestions for objectives like mean compliance, mean temperature, or model analysis. Some modern modeling technics in topology optimization require a nodal based material interpolation. Therefore this article is referred to a continuous material interpolation in topology optimization. To cover a smooth and differentiable density field, we address trigonometric shape functions which are infinitely differentiable. Furthermore, we extend a so-known global criteria method with a sharpening function based on binary cross-entropy, so that sharper solutions results. The proposed material interpolation is applied to different applications such as heat transfer, elasto static, and potential flow. Furthermore, these different objectives are together optimized using a multi-objective criterion.

Structural Topology Optimization Using Frame Elements Based on the Complementary Strain Energy Concept for Eigen-Frequency Maximization

2005 ◽  
Author(s):  
Akihiro Takezawa ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Topology Optimization ◽  
Cross Sections ◽  
Strain Energy ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Structural Topology ◽  
Energy Concept ◽  
Conceptual Design Phase ◽  
Complementary Strain ◽  
Topology Optimization Method

This paper discuses a new topology optimization method using frame elements for the design of mechanical structures at the conceptual design phase. The optimal configurations are determined by maximizing multiple eigen-frequencies in order to obtain the most stable structures for dynamic problems. The optimization problem is formulated using frame elements having ellipsoidal cross-sections, as the simplest case. Construction of the optimization procedure is based on CONLIN and the complementary strain energy concept. Finally, several examples are presented to confirm that the proposed method is useful for the topology optimization method discussed here.

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