Design 3D Thermo-Mechanical Structures with Multidisciplinary Topology Optimization

SUMMARYA method for topology optimization of continuum structures based on nodal density variables and density field mapping technique is investigated. The original discrete‐valued topology optimization problem is stated as an optimization problem with continuous design variables by introducing a material density field into the design domain. With the use of the Shepard family of interpolants, this density field is mapped onto the design space defined by a finite number of nodal density variables. The employed interpolation scheme has an explicit form and satisfies range‐restricted properties that makes it applicable for physically meaningful density interpolation. Its ability to resolve more complex spatial distribution of the material density within an individual element, as compared with the conventional elementwise design variable approach, actually provides certain regularization to the topology optimization problem. Numerical examples demonstrate the validity and applicability of the proposed formulation and numerical techniques. Copyright © 2011 John Wiley & Sons, Ltd.

Robust topology and discrete fiber orientation optimization under principal material uncertainty

With the rapid advancement of computing technology, mathematical modeling and computer simulations have become common and standard methods for design of complex systems. To exercise these models intelligently and eliminate the burden of manual iteration, manipulating inputs and reviewing outputs, optimization strategies are applied in a simulation-based design environment. In reality, the knowledge that engineers have about the design problem is imperfect and incomplete, uncertainty always exists in simulation-based design. The conventional deterministic optimization techniques do not consider the impact of such uncertainties. If the system responses driving the design decisions are very sensitive to these uncertainties, serious problems might confront the designer. Performance of the actual system may differ greatly from expected optimum performance. Again, if the design solution is near one or more constraint boundaries, then even slight uncertainties or changes in the operating environment could produce failed, unsafe designs, and/or result in substantial performance degradation. In recent years, the concept of reliability and robust design has become very popular. Probabilistic design analysis and statistical modeling allow the identification of designs that qualify as not only feasible, but as consistently feasible in the face of uncertainty. Reliability based topology optimization (RBTO) extends the reliability notion to the area of structural topology optimization. Although reliability based design optimization (RBDO) is a well established research area, very few work has been presented in the area of RBTO. In this study, we give an overview of the various works done in the field of RBTO. Ever since Bendsoe and Kikuchi introduced the topology optimization using a homogenization method, many topology optimization methods have been developed for the both linear and nonlinear structures. Traditional topology optimization methods drive the topology of a structure to an optimum design based on the constraint on mass. Kharmanda et al. introduced reliability constraints in deterministic topology optimization problem. They proposed a heuristic strategy that aims to reduce mass while improving the reliability level of the structure without greatly increasing its weight. But the limit state function used by them was not based on failure criteria for the structure. Their formulation considered uncertainty with respect to ∗Design Automation Laboratory †Advisor geometrical dimension and applied load only. Also their reliability analysis seems to be independent of the boundary and loading condition, so their results showed similar values for the uncertain variables for different structures. Tovar et al. have developed the Hybrid Cellular Automaton (HCA) method for structural synthesis of continuum material where the state of each cell is defined by both density and strain energy. In Agarwal, a decoupled RBDO approach is employed such that the topology optimization is separate from the reliability analysis. Patel et al. showed the use of RBTO using the gradient free Hybrid Cellular Automata (HCA) method. Their formulation incorporates uncertainty with respect to material property also. They considered limit state function based on failure modes on the output displacements. This study aims at giving a comparative study on these methods. It points out the advantages and disadvantages of the methods, and their significance in the field of RBTO. As large numbers of design variables are associated with continuum topology optimization problems, RBTO methods are inherently computationally expensive because of additional required system analysis associate with RBDO. Based on the observations, this study presents an efficient method for incorporating reliability analysis in topology optimization.

Free-mounted cooling plate multi-objective topology optimization method towards precision machine tool heat dissipation: An experimental and numerical study

Isogeometric analysis (IGA) connects CAE with standard CAD design tools and has been utilized for a decade in structural optimization. FEA has a number of drawbacks, including a lack of linkage between analytic and geometric models, a shortage of continuity between components, and a lack of accuracy for high-order elements. Isogeometric analysis effectively overcomes these obstacles. This paper proposes the isogeometric topological optimization mathematical model depending on the asymmetric constitutive relationship of tension and compression microscopic materials. We provide a new density-based topology optimization formulation in which the design domain is limited to the B-spline space. A rectangular domain with a tensor-product is embedded in a design domain that is arbitrarily shaped. The density field is represented using B-splines. The intrinsic filter provided by the B-spline representation for topology optimization is governed by the degrees of B-spline and the knot spans. This B-spline effectively removes numerical artifacts and controls the minimum feature-length in; when the B-spline basis functions span many analysis elements. Benchmark problems in structural topology optimization are computed through Evolutionary Structural Optimization (ESO) algorithm. Comparisons of the optimal structure topologies using finite element analysis and isogeometric collocation methods are analyzed. The influence of different tension-compression stiffness ratios on the final structure topologies is listed and analyzed. The numerical results show the reliability and performance of the proposed mathematical formulation and asymmetry of natural structure.

Topology optimization of pretensioned reflector antennas with unified cable-bar model

Topology optimization is gaining popularity as a primary tool for engineers in the initial stages of design. Essentially, the design domain is broken down into individual pixels, with the material density of each element or mesh point serving as a design variable. The optimization problem is then tackled through mathematical programming and optimization methods that rely on analytical gradient calculation. In this study, topology optimization using honeycomb tessellation elements is explored. Hexagonal elements have the ability to flexibly connect two adjacent elements. The use of the hexagonal element limits the occurrence of the checkerboard pattern to the finite elements of the quadrilateral standard Lagrangian type. A mathematical model is developed with the objective function being the minimum compliance value of the design domain. The element stiffness matrix is constructed using the strain-displacement matrix and the constitutive matrix, assuming a unit Young's modulus. Additionally, optimal conditions are established using Lagrangian multipliers. Two sensitivity and density filtering filters are employed to increase optimization efficiency, prevent the algorithm from reaching a local optimal state, and speed up convergence. If the suggested filter is employed, the objective function achieves a value of c=173,0293 and convergence is attained after 200 iterations. In contrast, without using the filter, the objective function has a larger value (c=186,7922) and convergence occurs at the 27th iteration. The results are significant for optimizing topology to meet specific boundary condition requirements. This paper proposes a novel approach using a combination of filters to advance topology optimization using hexagonal elements in future applications.

Self-consistent adjoint analysis for topology optimization of electromagnetic waves

An approach for the concurrent homogenization-based microstructure type and topology optimization problem

The density approach and the homogenization design method are representative methods in topology optimization problems. In the topology optimization in magnetic fields. those methods are applied based on the results of the applications in elastic fields. In this study. the density method is modified considering the concept of the homogenization design method. Also, the results of the topology optimization in magnetic fields by the modified density method as well as the homogenization method are compared especially focusing the change of the penalization parameter in the density approach. The effect of the definition of the design domain such as global/local design domain is also discussed.

A globally convergent method to accelerate topology optimization using on-the-fly model reduction

A robust topological derivative-based multi-material optimization approach: Optimality condition and computational algorithm

SummaryThe velocity field level‐set topological shape optimization method combines the implicit representation in the standard level‐set method and the capabilities of general mathematical programming algorithms in handling multiple constraints and additional design variables. The key concept is to construct the normal velocity field using basis functions and the velocity design variables at specified points (referred to as velocity knots) in the entire design domain. In this study, the velocity design variables are decoupled from the level‐set grid points. Making use of this property, we can adaptively change the arrangement of the velocity knots as the structural boundary evolves. This provides more design freedom in the optimization and allows for a significant reduction in the number of design variables. Several numerical examples in two‐ and three‐dimensional design domains are presented to demonstrate the robustness and efficiency of the proposed method. We also show that changing the number of velocity knots may implicitly exert certain control on topological complexity and length scale.

<div>A set of multidisciplinary topology optimization (MTO) and fast validation method is discussed, which can be applied in the car body concept design stage. First, considering seven typical loading cases, optimized load path is obtained by MTO. Then an equivalent car body model is built up with new load path. In order to verify its linear and nonlinear performances quickly, original and optimized path models are established, respectively, by using macro elements. The results show that rigidity and collision performance of the optimized path are better than that of the original one. In the meantime, reduce the validation time from hours to minutes.</div>

In this research, a reliability based topology optimization (RBTO) for structural design methodology using the Hybrid Cellular Automata (HCA) method is proposed. More speciflcally, a decoupled reliability based design optimization (RBDO) approach is utilized, so that the topology optimization is separate from the reliability analysis. In this paper, a maximum allowable displacement failure mode is considered. In this methodology, starting from a continuum design space of uniform material distribution and initial uncertain variable values, a deterministic topology optimization is followed by a reliability assessment of the resulting structure to determine the most probable point of failure (MPP) for the current structure. The MPP is determined with respect to the maximum allowable de∞ection of the structure when loaded. This is generally a computationally expensive process using traditional techniques due to the large number of design variables associated with topology optimization problem. However, combining the e‐cient methods of the non-gradient HCA algorithm with the decoupled approach for RBDO aims to reduce this burden. The topology optimization was without constraint in previous applications of the HCA method. To accommodate RTBO, a mechanism for a global constraint for maximum allowable displacement is developed. This paper details the methodology for the six-sigma design of structures using topology optimization.