基于多模型拓扑优化方法的车身结构概念设计

为获得最优的初始设计方案,在车身概念设计阶段对车身结构进行拓扑优化。车身结构性能指标综合考虑整体刚度、局部动态刚度和碰撞性能,采用多模型优化(multi-model optimization,MMO)方法解决此类复杂工况的拓扑优化问题,通过调节设计空间和设置参数,获得车身最优载荷路径。根据拓扑优化结果初步形成车身框架结构,可为后期详细设计提供参考。     

Conceptual design of aeroelastic structures by topology optimization

A topology optimization methodology is presented for the conceptual design of aeroelastic structures accounting for the fluid–structure interaction. The geometrical layout of the internal structure, such as the layout of stiffeners in a wing, is optimized by material topology optimization. The topology of the wet surface, that is, the fluid–structure interface, is not varied. The key components of the proposed methodology are a Sequential Augmented Lagrangian method for solving the resulting large-scale parameter optimization problem, a staggered procedure for computing the steady-state solution of the underlying nonlinear aeroelastic analysis problem, and an analytical adjoint method for evaluating the coupled aeroelastic sensitivities. The fluid–structure interaction problem is modeled by a three-field formulation that couples the structural displacements, the flow field, and the motion of the fluid mesh. The structural response is simulated by a three-dimensional finite element method, and the aerodynamic loads are predicted by a three-dimensional finite volume discretization of a nonlinear Euler flow. The proposed methodology is illustrated by the conceptual design of wing structures. The optimization results show the significant influence of the design dependency of the loads on the optimal layout of flexible structures when compared with results that assume a constant aerodynamic load.     

Level set based robust shape and topology optimization under random field uncertainties

A robust shape and topology optimization (RSTO) approach with consideration of random field uncertainty in loading and material properties is developed in this work. The proposed approach integrates the state-of-the-art level set methods for shape and topology optimization and the latest research development in design under uncertainty. To characterize the high-dimensional random-field uncertainty with a reduced set of random variables, the Karhunen–Loeve expansion is employed. The univariate dimension-reduction (UDR) method combined with Gauss-type quadrature sampling is then employed for calculating statistical moments of the design response. The combination of the above techniques greatly reduces the computational cost in evaluating the statistical moments and enables a semi-analytical approach that evaluates the shape sensitivity of the statistical moments using shape sensitivity at each quadrature node. The applications of our approach to structure and compliant mechanism designs show that the proposed RSTO method can lead to designs with completely different topologies and superior robustness.     

Simultaneous shape and topology optimization of shell structures

In this research, Method of Moving Asymptotes (MMA) is utilized for simultaneous shape and topology optimization of shell structures. It is shown that this approach is well matched with the large number of topology and shape design variables. The currently practiced technology for optimization is to find the topology first and then to refine the shape of structure. In this paper, the design parameters of shape and topology are optimized simultaneously in one go. In order to model and control the shape of free form shells, the NURBS (Non Uniform Rational B-Spline) technology is used. The optimization problem is considered as the minimization of mean compliance with the total material volume as active constraint and taking the shape and topology parameters as design variables. The material model employed for topology optimization is assumed to be the Solid Isotropic Material with Penalization (SIMP). Since the MMA optimization method requires derivatives of the objective function and the volume constraint with respect to the design variables, a sensitivity analysis is performed. Also, for alleviation of the instabilities such as mesh dependency and checkerboarding the convolution noise cleaning technique is employed. Finally, few examples taken from literature are presented to demonstrate the performance of the method and to study the effect of the proposed concurrent approach on the optimal design in comparison to the sequential topology and shape optimization methods.     

Conceptual and detailed design of an automotive engine cradle by using topology,shape, and size optimization

An automotive engine cradle supports many crucial components and systems, such as an engine, transmission, and suspension. Important performance measures for the design of an engine cradle include stiffness, natural frequency, and durability, while minimizing weight is of primary concern. This paper presents an effective and efficient methodology for engine cradle design from conceptual design to detailed design using design optimization. First, topology optimization was applied on a solid model which only contains the possible engine cradle design space, and an optimum conceptual design was determined which minimizes weight while satisfying all stiffness constraints. Based on topology optimization results, a design review was conducted, and a revised model was created which addresses all structural and manufacturability concerns. Shape and size optimization was then performed in the detailed design stage to further minimize the mass while meeting the stiffness and natural frequency targets. Lastly, the final design was validated for durability. The initial design domain had the mass of 82.6 kg; topology optimization in conceptual design reduced the mass to 26.7 kg; and the detailed design task involving shape and size optimization further reduced the mass to 21.4 kg.     

A new level-set based approach to shape and topology optimization under geometric uncertainty

Geometric uncertainty refers to the deviation of the geometric boundary from its ideal position, which may have a non-trivial impact on design performance. Since geometric uncertainty is embedded in the boundary which is dynamic and changes continuously in the optimization process, topology optimization under geometric uncertainty (TOGU) poses extreme difficulty to the already challenging topology optimization problems. This paper aims to solve this cutting-edge problem by integrating the latest developments in level set methods, design under uncertainty, and a newly developed mathematical framework for solving variational problems and partial differential equations that define mappings between different manifolds. There are several contributions of this work. First, geometric uncertainty is quantitatively modeled by combing level set equation with a random normal boundary velocity field characterized with a reduced set of random variables using the Karhunen–Loeve expansion. Multivariate Gauss quadrature is employed to propagate the geometric uncertainty, which also facilitates shape sensitivity analysis by transforming a TOGU problem into a weighted summation of deterministic topology optimization problems. Second, a PDE-based approach is employed to overcome the deficiency of conventional level set model which cannot explicitly maintain the point correspondences between the current and the perturbed boundaries. With the explicit point correspondences, shape sensitivity defined on different perturbed designs can be mapped back to the current design. The proposed method is demonstrated with a bench mark structural design. Robust designs achieved with the proposed TOGU method are compared with their deterministic counterparts.     

Simultaneous shape and topology optimization of prestressed concrete beams

This paper presents a new optimization approach for the design of prestressed concrete beams. The prestressing tendon is modeled as a chain of linear segments that transfer point forces to the concrete domain according to the tendon’s angles. The concrete beam is modeled as a discretized continuum following density-based approaches to topology optimization. The shape of the tendon and the topology of the surrounding concrete are optimized simultaneously within a single problem formulation. A special filtering technique is developed in order to ensure that the tendon is covered by concrete, thus shape and topological variables are tightly coupled. Several test cases demonstrate the applicability of the proposed optimization procedure. The deformation of the optimized designs due to external loads is counteracted by the deformation due to prestressing, hence by tuning the force in the tendon the total deformation can approach zero. Consequently, the beams exhibit a compression-only response meaning that the common goal of prestressed concrete design is achieved.     

Bubble method for topology and shape optimization of structures

This paper addresses a novel method of topology and shape optimization. The basic idea is the iterative positioning of new holes (so-called bubbles) into the present structure of the component. This concept is therefore called the bubble method. The iterative positioning of new bubbles is carried out by means of different methods, among others by solving a variational problem. The insertion of a new bubble leads to a change of the class of topology. For these different classes of topology, hierarchically structured shape optimizations that determine the optimal shape of the current bubble, as well as the other variable boundaries, are carried out.     

Combination of topology optimization and Lie derivative-based shape optimization for electro-mechanical design

Structural and Multidisciplinary Optimization - This paper presents a framework for the simultaneous application of shape and topology optimization in electro-mechanical design problems. Whereas...     

Semi-Lagrange method for level-set-based structural topology and shape optimization

In this paper, we introduce a semi-Lagrange scheme to solve the level-set equation in structural topology optimization. The level-set formulation of the problem expresses the optimization process as a solution to a Hamilton–Jacobi partial differential equation. It allows for the use of shape sensitivity to derive a speed function for a descent solution. However, numerical stability condition in the explicit upwind scheme for discrete level-set equation severely restricts the time step, requiring a large number of time steps for a numerical solution. To improve the numerical efficiency, we propose to employ a semi-Lagrange scheme to solve level-set equation. Therefore, a much larger time step can be obtained and a much smaller number of time steps are required. Numerical experiments comparing the semi-Lagrange method with the classical explicit upwind scheme are presented for the problem of mean compliance optimization in two dimensions.     

Experimental validation and prototyping of optimum designs obtained from topology optimization

This paper provides, through both numerical analyses and physical tests, a validation of the optimality of structural designs obtained from a topology optimization process. Issues related to the manufacturability of the topology-optimized design are first addressed in order to develop structural specimens suitable for experimental validation. Multidomain and multistep topology optimization techniques are introduced that, by embedding the designer’s intuition and experience into the design process, allow for the simplification of the design layout and thus for a better manufacturability of the design. A boundary identification method is also proposed that is applied to produce a smooth boundary for the design. An STL (STereo Lithography) file is then generated and used as input to a rapid prototyping machine, and physical specimens are fabricated for the experiments. Finally, the experimental measurements are compared with the theoretical and numerical predictions. Results agree extremely well for the example problems considered, and thus the optimum designs pass both virtual and physical tests. It is also shown that the optimum design obtained from topology optimization can be independent of the material used and the dimensions assumed for the structural design problem. This important feature extends the applicability of a single optimum design to a range of different designs of various sizes, and it simplifies the prototyping and experimental validation since small, inexpensive prototypes can be utilized. This could result in significant cost savings when carrying out proof-of-concept in the product development process.     

Simultaneous shape,topology, and homogenized properties optimization

In this brief note, we present an approach that combines the three classical techniques in structural optimization, i.e. the boundary variation and the topological and the homogenization methods. As a first test of this method, we apply it to the compliance opti-mization in .     

An additive manufacturing filter for topology optimization of print-ready designs

Additive manufacturing (AM) offers exciting opportunities to manufacture parts of unprecedented complexity. Topology optimization is essential to fully exploit this capability. However, AM processes have specific limitations as well. When these are not considered during design optimization, modifications are generally needed in post-processing, which add costs and reduce the optimized performance. This paper presents a filter that incorporates the main characteristics of a generic AM process, and that can easily be included in conventional density-based topology optimization procedures. Use of this filter ensures that optimized designs comply with typical geometrical AM restrictions. Its performance is illustrated on compliance minimization problems, and a 2D Matlab implementation is provided.     

Artificial neural network based hole image interpretation techniques for integrated topology and shape optimization

Homogenization based and density based topology optimization seeks the best conceptual structural configuration on a predefined design domain with specific boundary and loading conditions. Such structural configuration is most often the minimum-compliance design under a fixed material usage constraint. Shape optimization must be subsequently executed so as to ensure the satisfaction of other practical design constraints such as stress and displacement, and attain the detailed definition of the structure configuration with a smooth circumference and interior hole contours. Complicated procedures involved in connection between topology and shape optimization are major obstacle for most design engineers to overcome. A fully automated configuration optimization system was developed [C.Y. Lin, L.S. Chao, Automated image interpretation for integrated topology and shape optimization, Structural and Multidisciplinary Optimization 20(2) (2000) 125–137] to execute the entire configuration design process automatically with room of improvements in the hole representation templates and hole interpretation reliabilities. In response, this paper proposes two-stage artificial neural networks based hole image interpretation techniques with improved template variety and recognition reliability.     

A method for shape and topology optimization of truss-like structure

We present a method for the shape and topology optimization of truss-like structure. First, an initial design of a truss-like structure is constructed by a mesh generator of the finite element method because a truss-like structure can be described by a finite element mesh. Then, the shape and topology of the initial structure is optimized. In order to ensure a truss-like structure can be easily manufactured via intended techniques, we assume the beams have the same size of cross-section, and a method based on the concept of the SIMP method is used for the topology optimization. In addition, in order to prevent intersection of beams and zero-length beams, a geometric constraint based on the signed area of triangle is introduced to the shape optimization. The optimization method is verified by several 2D examples. Influence on compliance of the representative length of beams is investigated.     

Integrated optimal topology design and shape optimization using neural networks

In this paper, neural network- and feature-based approaches are introduced to overcome current shortcomings in the automated integration of topology design and shape optimization. The topology optimization results are reconstructed in terms of features, which consist of attributes required for automation and integration in subsequent applications. Features are defined as cost-efficient simple shapes for manufacturing. A neural network-based image-processing technique is presented to match the arbitrarily shaped holes inside the structure with predefined features. The effectiveness of the proposed approach in integrating topology design and shape optimization is demonstrated with several experimental examples.     

Concurrent shape and topology optimization for steady conjugate heat transfer

Structural and Multidisciplinary Optimization - Topology optimization is typically used to discover an optimized material distribution which implicitly defines the external shape of a body. The...     

Integration of topology and shape optimization for design of structural components

This paper presents an integrated approach that supports the topology optimization and CAD-based shape optimization. The main contribution of the paper is using the geometric reconstruction technique that is mathematically sound and error bounded for creating solid models of the topologically optimized structures with smooth geometric boundary. This geometric reconstruction method extends the integration to 3-D applications. In addition, commercial Computer-Aided Design (CAD), finite element analysis (FEA), optimization, and application software tools are incorporated to support the integrated optimization process. The integration is carried out by first converting the geometry of the topologically optimized structure into smooth and parametric B-spline curves and surfaces. The B-spline curves and surfaces are then imported into a parametric CAD environment to build solid models of the structure. The control point movements of the B-spline curves or surfaces are defined as design variables for shape optimization, in which CAD-based design velocity field computations, design sensitivity analysis (DSA), and nonlinear programming are performed. Both 2-D plane stress and 3-D solid examples are presented to demonstrate the proposed approach. Received January 27, 2000 Communicated by J. Sobieski