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Although various structural optimization techniques have a sound mathematical basis, the structural robustness and practical constructability of optimal designs pose a great challenge in the manufacturing stage. This paper presents an automated novel approach stemming from structural optimization and engineering principles, where discrete members of the structurally optimized designs are driven towards optimal utilization. The developed workflow unifies topology, layout and size optimization in a single parametric platform, which subsequently outputs a ready-to-manufacture CAD skeletal model which can be manufactured either additively or by assembly. All such outputs are checked and validated for structural requirements; strength, stiffness and stability in accordance with standard codes of practice. In the implementations, first, a topology-optimal model is generated and converted to a one-pixel-wide chain model using skeletonization. Herein, this paper uses a novel efficient method to extract the skeleton by using pixel-padding near the domain borders. Secondly, a spatial frame is extracted from the skeleton for its member size and layout optimization. Finally, the CAD model is generated using constructive solid geometry trees and the structural integrity of each member is assessed to ensure structural robustness prior to manufacturing. Various examples presented in the paper showcase the validity of the presented workflow across various structural engineering applications. • A novel method for design-informed structural optimisation is developed. • Handles both additive and assembly-based manufacturing techniques. • Optimal design outputs are structurally safe, stable and adequately-stiff. • Automated ready-to-manufacture CAD model outputs improve design efficiency. [ABSTRACT FROM AUTHOR]

A major difficulty in finite element analysis is the preparation of an effective mesh leading to a good response solution. In engineering analyses of complex components, oftentimes, much more time is spent to arrive at an adequate mesh than to obtain the solution of the established finite element model. The difficulty in meshing is due to the fact that finite elements need to abut each other and cannot overlap. This can lead to highly distorted elements, e.g. sliver elements, reducing the accuracy of solution. In practice, to establish an effective mesh, frequently, significant expertise in building meshes is needed, because great care must be taken in cleaning up the CAD geometry and preparing an effective mesh. The objective in this paper is to present a new finite element solution scheme including meshing in which the elements can overlap. The property that finite elements can overlap removes many of the meshing difficulties, leads to an effective meshing procedure and an overall easy-to-use solution scheme for an analyst or a designer. We first present the meshing scheme that we propose, which combines the use of traditional finite elements and overlapping finite elements. A particular feature is that the meshing procedure can be directly embedded in CAD driven solutions. We then present the theory used for the formulation of the overlapping finite elements and the coupling with traditional finite elements. We consider spherical and brick-shaped overlapping finite elements for which the theory is largely based on the formulation of the method of finite spheres. Finally, we illustrate the complete solution scheme in the analysis of some two-dimensional problems using the CAD geometry as the starting point. While the paper presents a new paradigm for analysis in CAD environments, with much potential, we realize that much further study and research is needed on some of the important ingredients of the method to render the complete procedure effective for general practical engineering analyses of static and dynamic problems. [ABSTRACT FROM AUTHOR]

Abstract: The concept of isogeometric analysis, whereby the parametric functions that are used to describe CAD geometry are also used to approximate the unknown fields in a numerical discretisation, has progressed rapidly in recent years. This paper advances the field further by outlining an isogeometric boundary element Method (IGABEM) that only requires a representation of the geometry of the domain for analysis, fitting neatly with the boundary representation provided completely by CAD. The method circumvents the requirement to generate a boundary mesh representing a significant step in reducing the gap between engineering design and analysis. The current paper focuses on implementation details of 2D IGABEM for elastostatic analysis with particular attention paid towards the differences over conventional boundary element implementations. Examples of Matlab® code are given whenever possible to aid understanding of the techniques used. [Copyright &y& Elsevier]

This paper investigates the performance of the global collocation method for the numerical eigenfrequency extraction of 2-D elastic structures. The method is applied to CAD-based macroelements, starting from the older blending function Coons-Gordon interpolation (based on Lagrange polynomials) and extending to tensor product Bézier and B-splines. Numerical findings show equivalence between Lagrangian and Bézierian macroelements, while a mass lumping procedure is proposed for the former ones. Concerning B-splines, the influence of multiplicity of inner knots and the position of collocation points is thoroughly investigated. The theory is supported by 2-D numerical examples on rectangular and curvilinear structures of simple shape under plane stress conditions, in which the approximate solution rapidly converges towards the exact solution faster than that of the conventional finite element of similar mesh density. [ABSTRACT FROM AUTHOR]

Recently, a global functional set has been proposed for the construction of large finite elements, here called “Coons-patch macroelements”, with degrees of freedom at the boundaries only. The background of the method is “Coons interpolation formula”; a mathematical formula capable of describing CAD surfaces initially applied to automobile applications. So far, these macroelements were found to be accurate in potential and plane elasticity problems. Based on these encouraging results, this paper continues the investigation on the universality which Coons interpolation formula offers in the development of a class of macroelements including members of the well-known serendipity family. In this context, it is shown in a systematic way that it is not necessary to use Lagrange polynomials to interpolate the potential along each side of the macroelement but one may choose piecewise-linear and/or cubic B-splines interpolants. Moreover, the paper investigates the performance of Coons-patch macroelements in eigenvalue and scalar wave propagation problems by implementing standard time-integration schemes. [Copyright &y& Elsevier]

This paper presents a Petrov–Galerkin natural element method for the nonlinear analysis of 2-D dynamic contact problems without friction. The frictionless dynamic contact problem is formulated according to the linearized total Lagrangian method incorporated with the linearized penalty method. The displacement increment is approximated with Laplace interpolation functions defined with the help of Voronoi polygons, while the admissible virtual displacement is expanded with constant strain functions which are supported on Delaunay triangles. The spatial numerical integration is carried out by applying the conventional Gauss quadrature rule to Delaunay triangles and the temporal time integration is performed by the implicit Newmark method. The validity of the proposed method is examined through the illustrating numerical experiments. [Copyright &y& Elsevier]

A moving rail vehicle may cause propagating waves to the surroundings potentially leading to detrimental effects for the track construction, nuisances for the surroundings and interference with delicate electronic equipment. A full computational model should be able to couple a correct simulation of the rigid body motion of the different train parts with accurate prediction of the solid wave propagation in the ground. This paper integrates the dynamics of the vehicle and the elastic soil into one monolithic system. Equations of motion for the train have been merged the system representing the FEM problem for the rest of the structure. Three models of modern high-speed locomotives were run over a solid finite element model of a rail structure. [Copyright &y& Elsevier]

Abstract: This paper introduces a new global functional set for the FEM solution of three-dimensional boundary-value problems. The main idea is to construct large isoparametric finite elements based on the interpolation formula, which was developed in 1960s by S.A. Coons for the numerical representation of arbitrary solid CAD regions bounded by six curvilinear surfaces. In this way, besides the geometry, Coons interpolation formula is used here for the global interpolation of the unknown potential within the whole solid region (problem area), a procedure that leads to large elements, called “macroelements”. For adequately smooth regions, the degrees of freedom appear only at the 12 boundary edges of the macroelement and can be used in the solution of both static (Laplace) and eigenvalue (acoustic) problems. The proposed approach is sustained by five numerical results where it is successfully compared with conventional finite elements and exact analytical solutions. [Copyright &y& Elsevier]

Abstract: Topology optimization result is usually a gray level image in discrete finite elements, which is hard to interpret from a design point of view. It is especially difficult to interpret three-dimensional topology optimization result. Although there are many techniques for interpreting topology optimization results, most of them only deal with two-dimensional problems, and some of the interpreting techniques must be performed manually. This paper presents an automated process for interpreting three-dimensional topology optimization result into a smooth CAD representation. A tuning process is employed before the interpretation process to improve the quality of the topology optimization result. In the tuning process, a continuity analysis is first used to transform the porous topology formed by the elements with intermediate densities in the topology optimization result into clear 0–1 elements. Next, trivial solids and trivial voids, which are useless in mechanics but will complicate the implementation of the interpretation process, are filtered out. After the tuning process, the three-dimensional structure is divided into representative cross-sections. On each cross-section, a density redistribution algorithm transfers the black-and-white finite element topology optimization result into a smooth density contour represented by B-spline curves on each cross-section. A three-dimensional CAD model is obtained by sweeping through these cross-sections. [Copyright &y& Elsevier]

A common characteristics in the simulation of automotive sheet metal forming processes is that nearly all die surfaces are manually created within conventional computer-aided design systems (CAD). The solutions produced using these CAD systems are undoubtedly valuable from the point of view of applicability in sheet metal forming practice. However, this approach is time consuming and most of the design time is spent within these CAD systems.This paper presents the development of a computer-based approach for the evolutionary automatic design (EAD) of geometry and process parameters for industrial metal forming processes. The main characteristics of the solution methodology are the use of evolution strategies within the optimizer, the use of sheet metal formability as objective functions and a parameterization of die surfaces. The results of a comparative study of our EAD die surface generation against conventional CAD die surface generation for a representative structural design problem show the efficiency of the former. It is observed that EAD often finds the region of the search space containing the global optimum, thus supporting engineers in practice with automatic generated sheet metal forming tools. [Copyright &y& Elsevier]

This paper presents an interactive method for the selection of design criteria and the formulation of optimization problems within a computer aided optimization process of engineering systems. The key component of the proposed method is the formulation of an inverse optimization problem for the purpose of determining the design preferences of the engineer. These preferences are identified based on an interactive modification of a preliminary optimization result that is the solution of an initial problem statement. A formulation of the inverse optimization problem is presented, which is based on a weighted-sum multi-objective approach and leads to an explicit optimization problem that is computationally inexpensive to solve. Numerical studies on structural shape optimization problems show that the proposed method is able to identify the optimization criteria and the formulation of the optimization problem which drive the interactive user modifications. [Copyright &y& Elsevier]