Moving Morphable Components Research Articles

Topology Optimization of a Three-Dimensional Flexible Multibody System Via Moving Morphable Components

In this work, an efficient topology optimization approach is proposed for a three-dimensional (3D) flexible multibody system (FMBS) undergoing both large overall motion and large deformation. The FMBS of concern is accurately modeled first via the solid element of the absolute nodal coordinate formulation (ANCF), which utilizes both nodal positions and nodal slopes as the generalized coordinates. Furthermore, the analytical formulae of the elastic force vector and the corresponding Jacobian are derived for efficient computation. To deal with the dynamics in the optimization process, the equivalent static load (ESL) method is employed to transform the topology optimization problem of dynamic response into a static one. Besides, the newly developed topology optimization method by moving morphable components (MMC) is used and reevaluated to optimize the 3D FMBS. In the MMC-based framework, a set of morphable structural components serves as the building blocks of optimization and hence greatly reduces the number of design variables. Therefore, the topology optimization approach has a potential to efficiently optimize an FMBS of large scale, especially in 3D cases. Two numerical examples are presented to validate the accuracy of the solid element of ANCF and the efficiency of the proposed optimization methodology, respectively.

Explicit isogeometric topology optimization using moving morphable components

We propose an explicit isogeometric topology optimization approach based on Moving Morphable Components (MMCs). The prescribed design domain is discretized using a NURBS patch and NURBS-based Isogeometric Analysis (IGA) method is adopted for structural response analysis and sensitivity analysis. We employ the MMCs to represent the geometries of structural components (a subset of the design domain) with use of explicit design parameters. The central coordinates, half-length, half-width, and inclined angles of MMCs are taken as design variables. The proposed method not only inherits the explicitness of the MMC-based topology optimization, but also embraces the merits of the Isogeometric Analysis (IGA) such as a tighter link with Computer-Aided Design (CAD) and higher-order continuity of the basis functions. Several numerical examples illustrate that the presented method based on IGA is more robust and stable than FEM-based topology optimization using MMCs.

Structural complexity control in topology optimization via moving morphable component (MMC) approach

In the present paper, an explicit method for controlling the structural complexity of continuum structures in topology optimization is proposed. This method is devised under the Moving Morphable Component (MMC) based framework where the geometries of the basic building blocks for topology optimization are described explicitly. Compared to the existing structural complexity control approaches which are generally developed in an implicit geometry/topology description framework, the proposed method allows an explicit definition of structural complexity, which facilitates the construction of the controlling schemes significantly. The effectiveness of the proposed method is demonstrated by numerical examples shown at the end of the paper.

Implementation of topological derivative in the moving morphable components approach

We propose a new topology optimization approach based on the moving morphable components (MMC) framework with an explicitly described a layout through a finite number of components. The position and shape values of each component were defined as design variables. In this study, a method was developed by utilizing topological derivative. Instead of performing a discrete sensitivity analysis based on finite element methods, a topological derivative was used to calculate the first derivative of an objective function with respect to the shape and position of the components. The obtained derivative was validated via discrete sensitivity analysis. The topological derivative formulation has been well developed in recent years for different structural and non-structural problems. Utilizing this powerful tool enabled the MMC approach to easily solve various types of topology optimization problems. Herein, the presented method is illustrated through several topology optimization problems such as stress-based and thermo-mechanical topology optimization.

Self-supporting structure design in additive manufacturing through explicit topology optimization

One of the challenging issues in additive manufacturing (AM) oriented topology optimization is how to design structures that are self-supportive in a manufacture process without introducing additional supporting materials. In the present contribution, it is intended to resolve this problem under an explicit topology optimization framework where optimal structural topology can be found by optimizing a set of explicit geometry parameters. Two solution approaches established based on the Moving Morphable Components (MMC) and Moving Morphable Voids (MMV) frameworks, respectively, are proposed and some theoretical issues associated with AM oriented topology optimization are also analyzed. Numerical examples provided demonstrate the effectiveness of the proposed methods.

A new three-dimensional topology optimization method based on moving morphable components (MMCs)

In the present paper, a new method for solving three-dimensional topology optimization problem is proposed. This method is constructed under the so-called moving morphable components based solution framework. The novel aspect of the proposed method is that a set of structural components is introduced to describe the topology of a three-dimensional structure and the optimal structural topology is found by optimizing the layout of the components explicitly. The standard finite element method with ersatz material is adopted for structural response analysis and the shape sensitivity analysis only need to be carried out along the structural boundary. Compared to the existing methods, the description of structural topology is totally independent of the finite element/finite difference resolution in the proposed solution framework and therefore the number of design variables can be reduced substantially. Some widely investigated benchmark examples, in the three-dimensional topology optimization designs, are presented to demonstrate the effectiveness of the proposed approach.

Structural Topology Optimization Through Explicit Boundary Evolution

Traditional topology optimization is usually carried out with approaches where structural boundaries are represented in an implicit way. The aim of the present paper is to develop a topology optimization framework where both the shape and topology of a structure can be obtained simultaneously through an explicit boundary description and evolution. To this end, B-spline curves are used to describe the boundaries of moving morphable components (MMCs) or moving morphable voids (MMVs) in the structure and some special techniques are developed to preserve the smoothness of the structural boundary when topological change occurs. Numerical examples show that optimal designs with smooth structural boundaries can be obtained successfully with the use of the proposed approach.

Minimum length scale control in structural topology optimization based on the Moving Morphable Components (MMC) approach

A novel approach, which can control the minimum length scale in topology optimization in a straightforward and explicit way, is proposed in the present paper. This approach is constructed under the so-called Moving Morphable Components (MMC) based solution framework where optimized structural topology can be found by changing the shapes and layout of a set of trapezoid-shaped structural components on a fixed finite element mesh. The eXtended Finite Element Method (XFEM) is employed for structural response analysis and shape sensitivity information is obtained by carrying out numerical integration along the structural boundary. A precision definition of the minimum length scale of a structure is also suggested based on the proposed solution framework. Compared with existing approaches, the proposed approach can achieve minimum length scale control by simply setting lower bounds on a set of geometric design variables. Only a small number of purely geometric constraints imposed on the sizes of intersection regions should be considered explicitly in order to get a complete minimum length scale control. Numerical examples demonstrate the effectiveness of the proposed method.

Explicit structural topology optimization based on moving morphable components (MMC) with curved skeletons

In the present paper, an explicit topology optimization approach based on moving morphable components (MMC) with curved skeletons (central lines) is proposed. This is achieved by constructing the topology description function (TDF) which describes the geometry of a structural component with curved skeleton explicitly in an elegant way. The proposed method has very flexible geometry modeling capability and represents a substantial improvement of the geometry modeling capability of existing MMC based approaches. Numerical examples demonstrate the effectiveness of the proposed approach.

Lagrangian Description Based Topology Optimization—A Revival of Shape Optimization

Unlike in the previous treatment where shape and topology optimization were carried out essentially in an Eulerian framework, the aim of the present work is to show how to perform topology optimization based on a Lagrangian framework, which is seamlessly consistent with classical shape optimization approaches, with use of a set of moving morphable components (MMCs). It is hoped that the present work may light up the revival of classical shape optimization in structural design and optimization and inspire some subsequent works along this direction. Some representative examples are also provided to illustrate the effectiveness of the proposed solution framework.

A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model

This paper presents a new topology optimization approach based on the so-called Moving Morphable Components (MMC) solution framework. The proposed method improves several weaknesses of the previous...