Structural and Multidisciplinary Optimization

This paper complements the analysis of geometric properties of the Hencky nets within the Michell cantilevers constructed in the trapezoidal domains by providing the analytical formulae for the force fields. The force field analysis introduces a new division of the cantilever domain and enables an alternative method for computing the optimal weights.

Parametric correlation exists widely in engineering problems. This paper presents an approach of evidence-theory-based design optimization (EBDO) with parametric correlations, which provides an effective computational tool for the structural reliability design involving epistemic uncertainties. According to the existing samples, the most fitting copula function is selected to formulate the joint basic probability assignment (BPA) of the correlated variables. The joint BPA is applied in the constraint reliability analysis, and an approximate technology is given to enhance the efficiency. A decoupling strategy is proposed for transforming the nested optimization of EBDO into a sequential iterative process of deterministic optimization and reliability analysis. The effectiveness of the proposed approach is demonstrated through two numerical examples and an engineering application.

The paper presents the crashworthiness optimization of a thin-walled frame applied as energy-absorbing element in a car structure. Crushing parameters of S-frame are modeled using the macro-element methodology. This method is implemented in the Visual Crash Studio software that enables very fast simulation of structural behavior during the impact. The objective is to determine the optimal dimensions of the frame cross-section to achieve the maximal energy absorption. Moreover, the selection of the best angle between the frame segments is investigated. In the formulation of the optimization problem, constraints related to the progressive collapse of deformation zones, required by the macro-element modeling, have been introduced. An Evolutionary Algorithm was applied to search the best solution. A real-life example of thin-walled S-frame is investigated in numerical examples. An attempt to find the solution by solving a sequence of simpler problems with reduced number of design variables is investigated. This approach is compared to the best result obtained for the problem including all design variables at the same time. This study illustrates the potential of the optimization in early-design stages of the vehicle development process and prepares perspectives for the optimization of complex energy-absorbing systems.

Crashworthiness of tailor-welded blank (TWB) structures signifies an increasing concern in lightweight design of vehicle. Although multiobjective optimization (MOO) has to a considerable extent been successfully applied to enhance crashworthiness of vehicular structures, majority of existing designs were restricted to single or uniform thin-walled components. Limited attention has been paid to such non-uniform components as TWB structures. In this paper, MOO of a multi-component TWB structure that involves both the B-pillar and inner door system subjected to a side impact, is proposed by considering the structural weight, intrusive displacements and velocity of the B-pillar component as objectives, and the thickness in different positions and the height of welding line of B-pillar as the design variables. The MOO problem is formulated by using a range of different metamodeling techniques, including response surface methodology (RSM), artificial neural network (ANN), radial basis functions (RBF), and Kriging (KRG), to approximate the sophisticated nonlinear responses. By comparison, it is found that the constructed metamodels based upon the radial basis function (RBF, especially multi-quadric model, namely RBF-MQ) fit to the design of experiment (DoE) checking points well and are employed to carry out the design optimization. The performance of the TWB B-pillar and indoor panel system can be improved by optimizing the thickness of the different parts and height of the welding line. This study demonstrated that the multi-component TWB structure can be optimized to further enhance the crashworthiness and reduce the weight, offering a new class of structural/material configuration for lightweight design.

Topology optimization for coupled acoustic-structural systems subjected to stationary random excitations is investigated. Bi-material elastic continuum structures without damping are considered. The finite element method is utilized to deal with coupled acoustic-structural problems. An accurate and highly efficient algorithm series for stationary random analysis techniques, pseudo excitation method, is extended to calculate the acoustic random response generated by the vibrating structures. Minimization of the auto power spectral density of sound pressure is taken as design objective and its sensitivities with respect to topological variables are derived by adjoint method. A penalty term is proposed to suppress the intermediate volumetric densities. Numerical examples are given to demonstrate the validity of the presented methods.

A new method is presented that combines heuristic global optimization and multi-model simulation for reliability based risk averse design. The so-called new stack ordering method is motivated from hydrogeology, where high-reliable groundwater management solutions are sought for with a demanding set of equally probable model alternatives. The idea is to only exploit a small subset of these model alternatives or realizations to approximate the objective function to reduce computational costs. The presented automatic procedure dynamically adjusts the subset online during the course of iterative optimization. The test with theoretical reliability based benchmark problems shows that the new method is efficient in regard to optimality and reliability of found solutions already with small subsets of all models. Compared with a previously presented first version of stack ordering, the presented generalized approach proves to be more robust, computationally efficient and of great potential for related problems in reliability based optimization and design. This conclusion is supported by the fact that the new variant requires about one fifth of the objective function evaluations of the older version in order to achieve the same level of reliability. We also show that these findings can be translated to real world problems by bench marking the performance on a well capture problem.

Optimal designs, and sensitivities of such designs, are calculated for transversely vibrating structures carrying an axially moving material. The structures studied consist of piecewise uniform and initially straight beam elements conveying a piecewise constant-speed plug flow of material along their deflected axes. The beams can be supported by a distributed Winkler-type ambient medium. Viscous damping in the beam material and the ambient medium is considered. Large static axial loads may act on the beam and on the moving material. The beams are modelled with a generalized second-order Rayleigh-Timoshenko theory including the Euler-Bernoulli theory as a special case. The structures investigated may also contain taut strings and rigid bodies. Considering a given subcritical material speed, the aim of the present study is to modify the initial design of a given beam structure in such a way that the transient vibrational motion following a transverse disturbance will die out as quickly as possible. To this end, complex eigenfrequencies pertaining to transverse vibration are calculated, and design parameters are changed so as to maximally raise the imaginary part of that eigenfrequency which has the smallest such part. In one of the examples, the objective is to maximally raise the product of the real and imaginary parts of the eigenfrequency which has the smallest such product.

We present a novel approach for efficient optimization of systems consisting of expensive to simulate components and relatively inexpensive system-level simulations. We consider the types of problem in which the components of the system problem are independent in the sense that they do not exchange coupling variables, however, design variables can be shared across components. Component metamodels are constructed using Kriging. The metamodels are adaptively sampled based on a system level infill sampling criterion using Efficient Global Optimization. The effectiveness of the technique is demonstrated by applying it on numerical examples and an engineering case study. Results show steady and fast converge to the global deterministic optimum of the problems.

This paper uses a dynamical systems approach for studying the material distribution (density or SIMP) formulation of topology optimization of structures. Such an approach means that an ordinary differential equation, such that the objective function is decreasing along a solution trajectory of this equation, is constructed. For stiffness optimization two differential equations with this property are considered. By simple explicit Euler approximations of these equations, together with projection techniques to satisfy box constraints, we obtain different iteration formulas. One of these formulas turns out to be the classical optimality criteria algorithm, which, thus, is receiving a new interpretation and framework. Based on this finding we suggest extensions of the optimality criteria algorithm. A second important feature of the dynamical systems approach, besides the purely algorithmic one, is that it points at a connection between optimization problems and natural evolution problems such as bone remodeling and damage evolution. This connection has been hinted at previously but, in the opinion of the authors, not been clearly stated since the dynamical systems concept was missing. To give an explicit example of an evolution problem that is in this way connected to an optimization problem, we study a model of bone remodeling. Numerical examples, related to both the algorithmic issue and the issue of natural evolution represented as bone remodeling, are presented.