An approach for geometrically nonlinear topology optimization using moving wide-Bézier components with constrained ends

2021 ◽  
pp. 1-15
Author(s):  
Benliang Zhu ◽  
Rixin Wang ◽  
Hongchuan Zhang ◽  
Hai Li ◽  
Junwen Liang ◽  
...  
Keyword(s):  
Topology Optimization ◽  
Structural Response ◽  
Optimization Methods ◽  
Response Analysis ◽  
Minimum Length ◽  
Geometrical Parameters ◽  
Geometrically Nonlinear ◽  
Structural Topology ◽  
Length Scale Control ◽  
Minimum Length Scale

Abstract Standard moving morphable component (MMC)-based topology optimization methods use free components with explicitly geometrical parameters as design units to obtain the optimal structural topology by moving, deforming and covering such components. In this study, we intend to present a method for geometrically nonlinear explicit topology optimization using moving wide Bezier components with constrained ends. Not only can the method efficiently avoid the convergence issues associated with nonlinear structural response analysis, but it can also alleviate the component disconnection issues associated with the standard MMC-based topology optimization methods. The numerical investigations proposed in this work indicate that the proposed method allows us to obtain results in accordance with the current literature with a more stable optimization process. In addition, the proposed method can easily achieve minimum length scale control without adding constraints.

Casting and Milling Restrictions in Topology Optimization via Projection-Based Algorithms

2012 ◽  
Author(s):  
James K. Guest ◽  
Mu Zhu
Keyword(s):  
Topology Optimization ◽  
Continuation Methods ◽  
Minimum Length ◽  
Manufacturing Constraints ◽  
Element Space ◽  
Structure Topology ◽  
Design Variables ◽  
Unstructured Meshing ◽  
Independent Design ◽  
Minimum Length Scale

Projection-based algorithms are arising as a powerful tool for continuum topology optimization. They use independent design variables that are projected onto element space to create structure topology. The projection functions are designed so that geometric properties, such as the minimum length scale of features, are naturally achieved. They therefore offer an efficient means for imposing geometry-related design specifications and/or manufacturing constraints. This paper presents recent advances in projection-based algorithms, including topology optimization under manufacturing constraints related to milling and casting processes. The new advancements leverage the logic of recently proposed algorithms for Heaviside projection, including eliminating continuation methods on projection parameters and potential for using multiple design variables to achieve active projection of each phase used in design. The primary advantages of such an approach are that manufacturing restrictions are achieved naturally, without need for additional constraints, and that sensitivity calculations are efficient and straightforward. The primary drawback of the approach is that the so-called neighborhood maps require storage for efficient processing when using unstructured meshing.

Gradient-Based Multi-Component Topology Optimization for Additive Manufacturing (MTO-A)

2017 ◽  
Author(s):  
Yuqing Zhou ◽  
Kazuhiro Saitou
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Simultaneous Optimization ◽  
Minimum Length ◽  
Manufacturing Constraints ◽  
Component Level ◽  
Component Size ◽  
Design Variables ◽  
Gradient Based ◽  
Minimum Length Scale

Topology optimization for additive manufacturing has been limited to the component-level designs with the component size smaller than the printer’s build volume. To enable the design of structures larger than the printer’s build volume, this paper presents a gradient-based multi-component topology optimization framework for structures assembled from components built by additive manufacturing. Constraints on component geometry for additive manufacturing are incorporated in the density-based topology optimization, with additional design variables specifying fractional component membership. For each component, constraints on build size, enclosed voids, overhangs, and the minimum length scale are imposed during the simultaneous optimization of overall base topology and component partitioning. The preliminary result on a minimum compliance structure shows promising advantages over the conventional monolithic topology optimization. Manufacturing constraints previously applied to monolithic topology optimization gain new interpretations when applied to multi-component assemblies, which can unlock richer design space for topology exploration.

Multiobjective Topology Optimization of Compliant Microgripper With Geometrically Nonlinearity

2007 ◽  
Author(s):  
Zhaokun Li ◽  
Xianmin Zhang
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Structural Response ◽  
Decision Function ◽  
Element Formulation ◽  
Geometrically Nonlinear ◽  
Conflicting Objectives ◽  
Incremental Scheme ◽  
Moving Asymptotes

Since compliant mechanism is usually required to perform in more than one environment, the ability to consider multiple objectives has to be included within the framework of topology optimization. And the topology optimization of micro-compliant mechanisms is actually a geometrically nonlinear problem. This paper deals with multiobjective topology optimization of micro-compliant mechanisms undergoing large deformation. The objective function is defined by the minimum compliance and maximum geometric advantage to design a mechanism which meets both stiffness and flexibility requirements. The weighted sum of conflicting objectives resulting from the norm method is used to generate the optimal compromise solutions, and the decision function is set to select the preferred solution. Geometrically nonlinear structural response is calculated using a Total-Lagrange finite element formulation and the equilibrium is found using an incremental scheme combined with Newton-Raphson iterations. The solid isotropic material with penalization approach is used in design of compliant mechanisms. The sensitivities of the objective functions are found with the adjoint method and the optimization problem is solved using the Method of Moving Asymptotes. These methods are further investigated and realized with the numerical example of compliant microgripper, which is simulated to show the availability of this approach proposed in this paper.

Sign in / Sign up

Export Citation Format

Share Document