Modelling issues of a holistic finite element approach in the virtual engineering design process

In the paper methods for the coupling of different meshed local domains of a product model, which occur in an adaptivity process are compared. The properties of the applied coupling methods are demonstrated on finite element models from structural mechanics to point out the advantages and disadvantages of the methods in a model adaptivity process in the field of automotive engineering. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Adaptive finite elements methods for virtual engineering design

The focus of this paper is the utilization of improved stresses on the surface of a construction for error estimation. The improved stresses are derived by using stress boundary conditions. They are applied for the calculation of recovered stresses required by the Zienkiewicz–Zhu error indicator. This approach leads to an enhancement of the error estimation on the boundary. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multi-scale modelling of sandwich structures using the Arlequin method Part I: Linear modelling

The paper presents an Arlequin based multi-scale method for studying problems related to the mechanical behaviour of sandwich composite structures. Towards this end, different models are mixed and glued to each other. Several coupling operators are tested in order to assess the usefulness of the proposed approach. A new coupling operator is proposed and tested on the different glued Arlequin zones. A free–clamped sandwich beam with soft core undergoing a concentrated effort on the free edge is used as a typical example (benchmark) in the validation procedure. Numerical simulations were conducted as the preliminary evaluation of the various coupling operators and the discrepancies between local and global models in the gluing zone have been addressed with sufficient care.     

Simultaneous engineering approach to an integrated design and process planning

To support integration of design and process planning, a reference model has been developed. This reference model represents the basis for a new methodology for integrated design and process planning which enables a Simultaneous Engineering approach in the early stages of product development. The reference model consists of four partial models. These are the activity model, the information model, the technical system model and the model of integrating methods. Using these models, the methodology enables a concurrent processing of design and process planning activities with regard to different components of a product. Furthermore, the methodology covers planning methods as well as execution methods, to support early transmission of information to downstream activities and a feedback of information to upstream activities within the process chain of design and process planning.     

Optimization in engineering design

This paper presents a method for solving a class of constrained optimization problems in finite-dimensional spaces. This type of problem usually arises in connection with parameter optimization in engineering design. Most often, these problems consist of incorporating upper and/or lower bounds on the variables in otherwise unconstrained optimization problems. The proposed method replaces the original optimization problem withm constraints (m>1) by a sequence of optimization problems with one constraint only. The theory behind this method is discussed in the subsequent sections.This research was supported by NSF Grant No. GK-4984.     

Application of lower bound direct method to engineering structures

Direct methods provide elegant and efficient approaches for the prediction of the long-term behaviour of engineering structures under arbitrary complex loading independent of the number of loading cycles. The lower bound direct method leads to a constrained non-linear convex problem in conjunction with finite element methods, which necessitates a very large number of optimization variables and a large amount of computer memory. To solve this large-scale optimization problem, we first reformulate it in a simpler equivalent convex program with easily exploitable sparsity structure. The interior point with DC regularization algorithm (IPDCA) using quasi definite matrix techniques is then used for its solution. The numerical results obtained by this algorithm will be compared with those obtained by general standard code Lancelot. They show the robustness, the efficiency of IPDCA and in particular its great superiority with respect to Lancelot.     

Explicit jump immersed interface method for virtual material design of the effective elastic moduli of composite materials

Virtual material design is the microscopic variation of materials in the computer, followed by the numerical evaluation of the effect of this variation on the material’s macroscopic properties. The goal of this procedure is an in some sense improved material. Here, we give examples regarding the dependence of the effective elastic moduli of a composite material on the geometry of the shape of an inclusion. A new approach on how to solve such interface problems avoids mesh generation and gives second order accurate results even in the vicinity of the interface. The Explicit Jump Immersed Interface Method is a finite difference method for elliptic partial differential equations that works on an equidistant Cartesian grid in spite of non-grid aligned discontinuities in equation parameters and solution. Near discontinuities, the standard finite difference approximations are modified by adding correction terms that involve jumps in the function and its derivatives. This work derives the correction terms for two dimensional linear elasticity with piecewise constant coefficients, i.e. for composite materials. It demonstrates numerically convergence and approximation properties of the method.      

Modified screening-based Kriging method with cross validation and application to engineering design

In this paper, a basis screening Kriging method using cross validation error is proposed to alleviate computational burden of the dynamic Kriging while maintaining its accuracy. Metamodeling is widely used for design optimization of complex engineering applications where considerable computation time is required. The Kriging method is one of popular metamodeling methods due to its accuracy and efficiency. There have been many attempts to improve accuracy of the Kriging method, and the dynamic Kriging method using cross-validation error, which selects adequate basis functions to best describe the mean structure of a response using a genetic algorithm, achieves outstanding performance in terms of accuracy. However, despite its accuracy, the dynamic Kriging requires very large amounts of computation because of the genetic algorithm and no limitation for order of basis functions. In the proposed method, a basis function set is determined by screening each basis function instead of using the genetic algorithm, which has advantages in computation for high dimensional metamodels or repeated metamodel generation. Numerical studies with four mathematical examples and two engineering applications verify that the proposed basis screening Kriging significantly reduces computation time with similar accuracy as the dynamic Kriging.     

Global optimization method using adaptive and parallel ensemble of surrogates for engineering design optimization

As a robust and efficient technique for global optimization, surrogate-based optimization method has been widely used in dealing with the complicated and computation-intensive engineering design optimization problems. It’s hard to select an appropriate surrogate model without knowing the behaviour of the real system a priori in most cases. To overcome this difficulty, a global optimization method using an adaptive and parallel ensemble of surrogates combining three representative surrogate models with optimized weight factors has been proposed. The selection of weight factors is treated as an optimization problem with the desired solution being one that minimizes the generalized mean square cross-validation error. The proposed optimization method is tested by considering several well-known numerical examples and one industrial problem compared with other optimization methods. The results show that the proposed optimization method can be a robust and efficient approach in surrogate-based optimization for locating the global optimum.     

Implementation of the virtual element method for coupled thermo-elasticity in Abaqus

Numerical Algorithms - In this paper, we employ the virtual element method for the numerical solution of linear thermo-elastic problems in two dimensions. The framework is implemented within the...     

Application of the sequential parametric convex approximation method to the design of robust trusses

We study an algorithm recently proposed, which is called sequential parametric approximation method, that finds the solution of a differentiable nonconvex optimization problem by solving a sequence of differentiable convex approximations from the original one. We show as well the global convergence of this method under weaker assumptions than those made in the literature. The optimization method is applied to the design of robust truss structures. The optimal structure of the model considered minimizes the total amount of material under mechanical equilibrium, displacements and stress constraints. Finally, Robust designs are found by considering load perturbations.     

The virtual element method in 50 lines of MATLAB

We present a 50-line MATLAB implementation of the lowest order virtual element method for the two-dimensional Poisson problem on general polygonal meshes. The matrix formulation of the method is discussed, along with the structure of the overall algorithm for computing with a virtual element method. The purpose of this software is primarily educational, to demonstrate how the key components of the method can be translated into code.     

THE RANDOM WEIGHTING APPROXIMATION FOR THE VIRTUAL SYSTEM METHOD

In this paper, the random weighting method is applied to the exponential system, and we construct the approximation to the estimates of the system parameters with an accuracy of o(n^-1/2) as n→∞.     

Optimal product design using a colony of virtual ants

The optimal product design problem, where the “best” mix of product features are formulated into an ideal offering, is formulated using ant colony optimization (ACO). Here, algorithms based on the behavior of social insects are applied to a consumer decision model designed to guide new product decisions and to allow planning and evaluation of product offering scenarios.     

Optimal testing strategies in overlapped design process

Testing is an important activity in product development. Past studies, which are developed to determine the optimal scheduling of tests, often focused on single-stage testing of sequential design process. This paper presents an analytical model for the scheduling of tests in overlapped design process, where a downstream stage starts before the completion of upstream testing. We derive optimal stopping rules for upstream and downstream stages’ testing, together with the optimal time elapsed between beginning the upstream tests and beginning the downstream development. We find that the cost function is first convex then concave increasing with respect to upstream testing duration. A one-dimensional search algorithm is then proposed for finding the unique optimum that minimizes the overall cost. Moreover, the impact of different model parameters, such as the problem-solving capacity and opportunity cost, on the optimal solution is discussed. Finally, we compare the testing strategies in overlapped process with those in sequential process, and get some additional results. The methodology is illustrated with a case study at a handset design company.     

On the solution of large engineering design problems via mathematical programming

The method of moving asymptotes (MMA) is known to work well for the solution of mathematical programs arising in engineering design problems. Recently, the method has been extended by using two interior point approaches for the solution of the arising convex subproblems. Besides function and gradient evaluations, i.e. finite element analyses, the main computational work has to be done in the solution of a large sequence of linear systems. The interior point approach provides more flexibility in the formulation of these systems which is advantageous for large scale applications.