Rigorous global optimization of impulsive planet-to-planet transfers in the patched-conics approximation

The rigorous solution of a generic impulsive planet-to-planet transfer by means of a Taylor-model-based global optimizer is presented. Although a planet-to-planet transfer represents the simplest case of interplanetary transfer, its formulation and solution is a challenging task when the rigorous global optimum is sought. A customized ephemeris function is derived from JPL DE405 to allow the Taylor-model evaluation of planets’ positions and velocities. Furthermore, the validated solution of Lambert's problem is addressed for the rigorous computation of transfer fuel consumption. The optimization problem, which consists in finding the optimal launch and transfer time to minimize the required fuel mass, is complex due to the abundance of local minima and relatively high search-space dimension. Its rigorous solution by means of the Taylor-model-based global optimizer COSY-GO is presented considering Earth–Mars and Earth–Venus transfers as test cases.     

Design synthesis and structural optimization of a lightweight,monobloc cast iron brake disc with fingered hub

This article focuses on generating a monobloc fingered hub (top-hat) disc design, aiming at reducing disc mass but maintaining rotor thermal capacity, while also improving heat dissipation characteristics. The analyses and tests demonstrated that such a design is possible to achieve, with mass reduction of just over 9%. The activities included research into cast iron modelling, which gave very important insights into the limits of mechanical performance under bending. Initial finite element analyses enabled considerable progress to be made towards establishing a baseline design, but only through shape optimization and topology optimization procedures was the full potential of the design accomplished. Shape optimization facilitated the reduction of maximum principal stress by 32%, considerably improving disc torsional strength with practically no increase in mass. The safety factor in torsion achieved a value of 3.57. Topology optimization provided further, although small, mass reduction (1.5%) while maintaining low stress levels.     

A projection-based method for topology optimization of structures with graded surfaces

Graded surfaces widely exist in natural structures and inspire engineers to apply functionally graded (FG) materials to cover structural surfaces for performance improvement, protection, or other special functionalities. However, how to design such structures with FG surfaces by topology optimization is a quite challenging problem due to the difficulty for determining material properties of structural surfaces with prescribed variation rule. This paper presents a novel projection-based method for topology optimization of this class of FG structures. Firstly, a projection process is proposed for ensuring the material properties of the surfaces vary with a prescribed function. A criterion of determining the values of parameters in projection process is given by a strict theoretical derivation, and then, a new interpolation function is established, which is capable of simultaneously obtaining clear substrate topologies and realizable FG surfaces. Though such structures are actually multimaterial gradient structures, only the design variables of single-material topology optimization problem are needed. In the current research, the classical compliance minimization problem with a mass constraint is considered and the robust formulation is used to control the length scale of substrates. Several 2D and 3D numerical examples illustrate the validity and applicability of the proposed method.     

Design of dissipative multimaterial viscoelastic-hyperelastic systems at finite strains via topology optimization

This study focuses on the topology optimization framework for the design of multimaterial dissipative systems at finite strains. The overall goal is to combine a soft viscoelastic material with a stiff hyperelastic material for realizing optimal structural designs with tailored damping and stiffness characteristics. To this end, several challenges associated with incorporating finite-deformation viscoelastic-hyperelastic materials in a multimaterial design framework are addressed. This includes consideration of a thermodynamically consistent finite-strain viscoelasticity model for simulating energy dissipation together with F-bar finite elements for handling material incompressibility. Moreover, an effective multimaterial interpolation scheme is proposed, which preserves the physics of material mixtures in the context of density-based topology optimization. A numerically accurate analytical design sensitivity calculation is also presented using a path-dependent adjoint method. Furthermore, both prescribed-load and prescribed-displacement boundary conditions are considered in the optimization formulations, together with various strategies for controlling stiffness. As demonstrated by the numerical examples, the use of the stiffer hyperelastic material phase in a design not only improves stiffness but also increases energy dissipation capacity. Moreover, with the finite-deformation theory, the effect of the loading magnitude on the optimized designs can be observed.     

Topology optimization of a magnetic field in a three-dimensional finite region

This article describes the method of magnetic field topology optimization in an axisymmetric three-dimensional finite region. It is assumed that the region of interest is surrounded by a cylindrical solenoid with an electrical current. The solenoid’s inner and outer surfaces are built-up by rotating plane Bezier curves around the symmetry axis. As a global minimizer a genetic algorithm method is used. Optimal configurations are provided under given constraints.     

Topology optimization of multiscale elastoviscoplastic structures

This paper extends current concepts of topology optimization to the design of structures made of nonlinear microheterogeneous materials. The objective is to maximize the macroscopic structural stiffness for a prescribed material volume usage while accounting for the nonlinearity and the microstructure of the material. The resulting design problem considers two scales: the macroscopic scale at which the optimization is performed and the microscopic scale at which the material heterogeneities and the nonlinearities are observed. The topology optimization at the macroscopic scale is performed by means of the bi‐directional evolutionary structural optimization method. The solution of the macroscopic boundary value problem requires as inputs the effective constitutive response with full consideration of the microstructure. While computational homogenization methods such as the FE² method could be used to solve the nonlinear multiscale problem, the associated numerical expense (CPU time and memory) is highly unacceptable. In order to regain the computational feasibility of the computational scale transition, a recent model reduction technique of the authors is employed: the potential‐based reduced basis model order reduction with graphics processing unit acceleration. Numerical examples show the efficiency of the resulting nonlinear two‐scale designs. The impact of different load amplitudes on the design is examined. Copyright © 2015 John Wiley & Sons, Ltd.     

Geometry and topology optimization of sheet metal profiles by using a branch‐and‐bound framework

In this paper well established procedures from partial differential equation (PDE)‐constrained and discrete optimization are combined in a new way to find an optimal design of a multi‐chambered profile. Given a starting profile design, a load case and corresponding design constraints (e.g. sheet thickness, chamber sizes), the aim is to find an optimal subdivision into a predefined number of chambers with optimal shape subject to structural stiffness. In the presented optimization scheme a branch‐and‐bound tree is generated with one additional chamber in each level. Before adding the next chamber, the geometry of the profile is optimized. Then a relaxation of a topology optimization problem is solved. Based on this relaxation, a best fitting feasible topology subject to manufacturability conditions is determined using a new mixed integer method employing shortest paths. To improve the running time, the finite element simulations for the geometry optimization and topology relaxation are performed with different levels of accuracy. Finally, numerical experiments are presented including different starting geometries, load scenarios and mesh sizes.