Topology Optimization of Structures Using a Global Stress Measure

2012 ◽  
Author(s):  
Vijay Krishna Yalamanchili ◽  
Ashok V. Kumar
Keyword(s):  
Topology Optimization ◽  
Objective Function ◽  
Continuous Distribution ◽  
Stress Constraints ◽  
Von Mises Stress ◽  
Feasible Region ◽  
Barrier Method ◽  
Stress Measure ◽  
Global Stress ◽  
Mean Compliance

An approach for stress based topology optimization is studied here where stress constraints for continuum structures are imposed using a conservative global stress measure. A relation between the mean compliance and Von-Mises stress is used to construct an objective function that minimizes mass until stress constraints are activated. This approach is implemented in a mesh independent finite element framework where the feasible region is defined using boundary equations while analysis and topology optimization are performed on a background mesh. The SIMP approach is used for topology optimization and nodal values of density are treated as the design variables. The density field is interpolated over the elements to obtain a continuous distribution. To ensure smooth boundaries a smoothing term is also added to the objective function which minimizes gradient of the density function. The optimization problem is then solved using Moving Barrier Method (MBM). Several examples are studied to evaluate this approach.

scholarly journals On the Topology Optimization of Elastic Supporting Structures under Thermomechanical Loads

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Jie Hou ◽  
Ji-Hong Zhu ◽  
Qing Li
Keyword(s):  
Topology Optimization ◽  
Adjoint Method ◽  
Stress Constraints ◽  
Optimized Design ◽  
Elastic Supports ◽  
Domain Optimization ◽  
Stress Measure ◽  
Optimization Formulation ◽  
Global Stress ◽  
Supporting Structures

This paper is to present a thermomechanical topology optimization formulation. By designing structures that support specific nondesignable domain, optimization is to suppress the stress level in the nondesignable domain and maintain global stiffness simultaneously. A global stress measure based onp-norm function is then utilized to reduce the number of stress constraints in topology optimization. Sensitivity analysis employs adjoint method to derive the global stress measure with respect to the topological pseudodensity variables. Some particular behaviors in thermomechanical topology optimization of elastic supports, such as the influence of different thermomechanical loads and the existence of intermediate material, are also analyzed numerically. Finally, examples of elastic supports on a cantilever beam and a nozzle flap under different thermomechanical loads are tested with reasonable optimized design obtained.

Design of flexure hinges based on stress-constrained topology optimization

2016 ◽  
Vol 231 (24) ◽  
pp. 4635-4645 ◽  
Author(s):  
Min Liu ◽  
Xianmin Zhang ◽  
Sergej Fatikow
Keyword(s):  
Topology Optimization ◽  
Stress Concentration ◽  
Stress Constraints ◽  
Stress Constraint ◽  
Flexure Hinges ◽  
Weighted Sum Method ◽  
Stress Measure ◽  
Von Mises ◽  
Von Mises Stresses ◽  
Sharp Corners

Stress concentration is one of the disadvantages of flexure hinges. It limits the range of motion and reduces the fatigue life of mechanisms. This article designs flexure hinges by using stress-constrained topology optimization. A weighted-sum method is used for converting the multi-objective topology optimization of flexure hinges into a single-objective problem. The objective function is presented by considering the compliance factors of flexure hinges in the desired and other directions. The stress constraint and other constraint conditions are developed. An adaptive normalization of the P-norm of the effective von Mises stresses is adopted to approximate the maximum stress, and a global stress measure is used to control the stress level of flexure hinges. Several numerical examples are performed to indicate the validity of the method. The stress levels of flexure hinges without and with stress constraints are compared. In addition, the effects of mesh refinement and output spring stiffness on the topology results are investigated. The stress constraint effectively eliminates the sharp corners and reduces the stress concentration.

Topology optimization of structures subject to self-weight loading under stress constraints

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Renatha Batista dos Santos ◽  
Cinthia Gomes Lopes
Keyword(s):  
Topology Optimization ◽  
Stress Constraints ◽  
Topological Derivative ◽  
The Self ◽  
Von Mises Stress ◽  
Stress Constraint ◽  
Content Type ◽  
Derivative Method ◽  
Von Mises ◽  
Weight Loading

PurposeThe purpose of this paper is to present an approach for structural weight minimization under von Mises stress constraints and self-weight loading based on the topological derivative method. Although self-weight loading topology has been the subject of intense research, mainly compliance minimization has been addressed.Design/methodology/approachThe resulting minimization problem is solved with the help of the topological derivative method, which allows the development of efficient and robust topology optimization algorithms. Then, the derived result is used together with a level-set domain representation method to devise a topology design algorithm.FindingsNumerical examples are presented, showing the effectiveness of the proposed approach in solving a structural topology optimization problem under self-weight loading and stress constraint. When the self-weight loading is dominant, the presence of the regularizing term in the formulation is crucial for the design process.Originality/valueThe novelty of this research work lies in the use of a regularized formulation to deal with the presence of the self-weight loading combined with a penalization function to treat the von Mises stress constraint.

scholarly journals Topological Design of Multi-Material Compliant Mechanisms with Global Stress Constraints

Micromachines ◽  
2021 ◽  
Vol 12 (11) ◽  
pp. 1379
Author(s):  
Jinqing Zhan ◽  
Yifeng Li ◽  
Zhen Luo ◽  
Min Liu
Keyword(s):  
Compliant Mechanisms ◽  
Stress Constraints ◽  
Von Mises Stress ◽  
Stress Constraint ◽  
Output Displacement ◽  
Topological Design ◽  
Global Stress ◽  
Von Mises ◽  
Moving Asymptotes ◽  
Structural Volume

This paper presents an approach for the topological design of multi-material compliant mechanisms with global stress constraints. The element stacking method and the separable stress interpolation scheme are applied to calculate the element stiffness and element stress of multi-material structures. The output displacement of multi-material compliant mechanisms is maximized under the constraints of the maximum stress and the structural volume of each material. The modified P-norm method is applied to aggregate the local von Mises stress constraints for all the finite elements to a global stress constraint. The sensitivities are calculated by the adjoint method, and the method of moving asymptotes is utilized to update the optimization problem. Several numerical examples are presented to demonstrate the effectiveness of the proposed method. The appearance of the de facto hinges in the optimal mechanisms can be suppressed effectively by using the topology optimization model with global stress constraints, and the stress constraints for each material can be met.

Topology Optimization and Digital Manufacturing of Stress-Constrained Structure Based on Level Set Method

2014 ◽  
Vol 556-562 ◽  
pp. 4202-4205
Author(s):  
Yao Yao Xiu ◽  
Sen Liang
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Electrical Discharge Machining ◽  
Von Mises Stress ◽  
Stress Constraint ◽  
Digital Manufacturing ◽  
Programming Technique ◽  
Material Derivative ◽  
Mean Compliance

A theoretical model of stress-constrained topology optimization is established via level set method, a novel sensitivity analysis for the mean compliance with the stress constraint of the global measure of von Mises stress is derived by the material derivative. The triangle plane method and the Delaunay triangulation are explored to extract and sort the boundary point-cloud data, respectively. Digital manufacturing of optimization result is accomplished by automatically programming technique and wire electrical-discharge machining. Numerical examples of two-dimensional cantilever beam structure show the validity of the proposed method of this present work.

scholarly journals Topology Optimization of Hard-Coating Thin Plate for Maximizing Modal Loss Factors

Coatings ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 774
Author(s):  
Haitao Luo ◽  
Rong Chen ◽  
Siwei Guo ◽  
Jia Fu
Keyword(s):  
Topology Optimization ◽  
Objective Function ◽  
Composite Plates ◽  
Optimization Method ◽  
Hard Coating ◽  
Design Variables ◽  
Coating Composite ◽  
Damping Materials ◽  
Topology Optimization Method ◽  
Loss Factors

At present, hard coating structures are widely studied as a new passive damping method. Generally, the hard coating material is completely covered on the surface of the thin-walled structure, but the local coverage cannot only achieve better vibration reduction effect, but also save the material and processing costs. In this paper, a topology optimization method for hard coated composite plates is proposed to maximize the modal loss factors. The finite element dynamic model of hard coating composite plate is established. The topology optimization model is established with the energy ratio of hard coating layer to base layer as the objective function and the amount of damping material as the constraint condition. The sensitivity expression of the objective function to the design variables is derived, and the iteration of the design variables is realized by the Method of Moving Asymptote (MMA). Several numerical examples are provided to demonstrate that this method can obtain the optimal layout of damping materials for hard coating composite plates. The results show that the damping materials are mainly distributed in the area where the stored modal strain energy is large, which is consistent with the traditional design method. Finally, based on the numerical results, the experimental study of local hard coating composites plate is carried out. The results show that the topology optimization method can significantly reduce the frequency response amplitude while reducing the amount of damping materials, which shows the feasibility and effectiveness of the method.

scholarly journals Research on the inverse kinematics of manipulator using an improved self-adaptive mutation differential evolution algorithm

2021 ◽  
Vol 18 (3) ◽  
pp. 172988142110144
Author(s):  
Qianqian Zhang ◽  
Daqing Wang ◽  
Lifu Gao
Keyword(s):  
Differential Evolution ◽  
Objective Function ◽  
Inverse Kinematics ◽  
Differential Evolution Algorithm ◽  
Weight Coefficient ◽  
Adaptive Mutation ◽  
Feasible Region ◽  
Serial Manipulators ◽  
De Algorithm ◽  
Self Adaptive

To assess the inverse kinematics (IK) of multiple degree-of-freedom (DOF) serial manipulators, this article proposes a method for solving the IK of manipulators using an improved self-adaptive mutation differential evolution (DE) algorithm. First, based on the self-adaptive DE algorithm, a new adaptive mutation operator and adaptive scaling factor are proposed to change the control parameters and differential strategy of the DE algorithm. Then, an error-related weight coefficient of the objective function is proposed to balance the weight of the position error and orientation error in the objective function. Finally, the proposed method is verified by the benchmark function, the 6-DOF and 7-DOF serial manipulator model. Experimental results show that the improvement of the algorithm and improved objective function can significantly improve the accuracy of the IK. For the specified points and random points in the feasible region, the proportion of accuracy meeting the specified requirements is increased by 22.5% and 28.7%, respectively.

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