Abstract: Topology optimization (TO) has become an integral part of the structural design process in recent years. However, automatically deriving parametrized Computer-Aided Design (CAD) models from TO results still represents a great challenge. In this paper, we present a new fully automatic process aimed at converting 3D TO results that tend towards beam-like structures into solid CAD models. Our reconstruction process starts with curve-skeletonization of the optimized shape. The curve-skeleton obtained is used alongside with a boundary triangulation of the optimized shape to compute closed cross-sections along the skeleton branches and junctions at the intersection between branches. These cross-sections are interpolated with cubic B-spline fitting curves, which are used as a basis for lofting operations to generate CAD surface representations of branches and junctions of the optimized shape. Remaining openings in the optimized shape boundary are closed with filling surfaces. A solid CAD model can be built by sewing together all created surfaces and filling, by the way, the closed boundary that comes out of this process. Finite Element Analysis (FEA) is carried out on both the 3D optimal shape and the CAD solid model derived in order to validate this CAD model. Several case studies are presented to demonstrate effectiveness and usefulness of this new approach. • Reconstruction of 3D solid models from topology optimization results. • Based on curve-skeletonization, B-spline fitting curves and lofting operations. • Applied to beam-like topology optimization results. • FEA validation of 3D models generated.

Abstract: This paper presents an efficient constraint-handling technique (CHT) for metaheuristic algorithms in the size and shape optimization of truss structures. During the search process, the proposed CHT utilizes an improved Deb rule to filter redundant structural analyses and maps the candidate designs onto the feasible boundary for structural optimization to improve its search ability and stability based on the mapping strategy. The performance of the newly developed Manta Ray Foraging Optimization (MRFO) algorithm using the proposed CHT in structural optimization was also examined. Five truss optimization problems are used to examine the efficiency of the hybrid CHT compared with the improved Deb rule, the EDP method, and the mapping strategy. Four widely used metaheuristic algorithms, including HS, PSO, TLBO, and CS, have also been used to evaluate the performance of the MRFO in structural optimization. Numerical results demonstrate that the hybrid CHT can markedly improve both the search capacity and computational efficiency of metaheuristic algorithms. The MRFO does not show obvious weakness compared with existing algorithms in structural optimization. A comparison analysis also shows that the performances of the hybrid CHT vary across optimization algorithms.

Abstract: The standard geometries of dished ends of cylindrical pressure vessels were developed at the beginning of the last century. Among them, there are ellipsoidal and torispherical geometries characterized by disadvantageous stress distribution, which is the primary determinant when designing shell structures. This paper focuses on shape optimization of dished ends with the depth equivalent to the standard ones, with the intent to minimize the maximum von Mises stress in a cylindrical pressure vessel. Referring to the Bézier curve (BC), a unique geometry of arbitrary order is developed to describe the parametric shape of the dished end. The optimization is implemented using two approaches. Initially, the fitness function is obtained analytically through the membrane theory (MT). A deterministic optimization algorithm is adopted to complete the procedure. Further, the optimization method is modified to obtain the fitness function using the finite element method (FEM). To process the solution, a genetic algorithm (GA) is employed. The obtained improvement of stress distribution is compelling while maintaining the manufacturability of the shell structure.

Abstract: Structural curved metal dampers are implemented in various applications to mitigate the damages at a specific area efficiently. A stable and saturated hysteretic behavior for the in-plane direction is dependent on the shape of a curved-shaped damper. However, it has been experimentally shown that the hysteretic behavior in the conventional curved-shaped damper is unstable, mainly as a result of bi-directional deformations. Therefore, it is necessary to conduct shape optimization for curved dampers to enhance their hysteretic behavior and energy dissipation capability. In this study, the finite element (FE) model built in ABAQUS, is utilized to obtain optimal shape for the curved-shaped damper. The effectiveness of the model is checked by comparisons of the FE model and experimental results. The parameters for the optimization include the curved length and shape of the damper, and the improved approach is conducted by investigating the curved sections. In addition, the design parameters are represented by B-spline curves (to ensure enhanced system performance), regression analysis is implemented to derive optimization formulations considering energy dissipation, constitutive material model, and cumulative plastic strain. Results determine that the energy dissipation capacity of the curved steel damper could be improved by 32% using shape optimization techniques compared to the conventional dampers. Ultimately, the study proposes simple optimal shapes for further implementations in practical designs.

Abstract: This paper presents a shape optimisation system to design the shape of an acoustically-hard object in the three-dimensional open space. The boundary element method (BEM) is suitable to analyse such an exterior field. However, the conventional BEM, which is based on piecewise polynomial shape and approximate (interpolation) functions, can require many design variables because they are usually chosen as a part of the nodes of the underlying boundary element mesh. In addition, it is not easy for the conventional method to compute the gradient of the sound pressure on the surface, which is necessary to compute the shape derivative of our interest, of a given object. To overcome these issues, we employ the isogeometric boundary element method (IGBEM), which was developed in our previous work. With using the IGBEM, we can design the shape of surfaces through control points of the NURBS surfaces of the target object. We integrate the IGBEM with the nonlinear programming software through the adjoint variable method (AVM), where the resulting adjoint boundary value problem can be also solved by the IGBEM with a slight modification. The numerical verification and demonstration validate our shape optimisation framework.

Abstract: Composite tape-spring hinge (CTSH) is a simple yet elegant mechanical component for various deployable space structures. This paper formulates and addresses cut-out shape optimization of a CTSH, which is seldom touched upon in literature. Both the maximum strain energy stored during the folding process as well as the maximum bending moment during deployment were maximized in a concurrent way, and the multi-objective optimization problem was realized by merging data-driven surrogate modeling and shape optimization. Four different surrogate modeling techniques (radial basis function, kriging, Gaussian process regression, and artificial neural network) are evaluated and compared. The maximum stored strain energy at the fully folded state and the maximum bending moment during deployment for the optimal CTSH are increased by 50 and 35%, respectively, compared to the initial design under a previously developed composite failure criterion as constraint. To ensure reproducibility and foster future research, we publicly share our full implementation with the source codes and trained models with the community.

Abstract: This article introduces a novel method for the implementation of shape optimisation with Lipschitz domains. We propose to use the shape derivative to determine deformation fields which represent steepest descent directions of the shape functional in the W 1, ∞ -topology. The idea of our approach is demonstrated for shape optimisation of n -dimensional star-shaped domains, which we represent as functions defined on the unit ( n − 1)-sphere. In this setting we provide the specific form of the shape derivative and prove the existence of solutions to the underlying shape optimisation problem. Moreover, we show the existence of a direction of steepest descent in the W 1, ∞ − topology. We also note that shape optimisation in this context is closely related to the ∞ −Laplacian, and to optimal transport, where we highlight the latter in the numerics section. We present several numerical experiments in two dimensions illustrating that our approach seems to be superior over a widely used Hilbert space method in the considered examples, in particular in developing optimised shapes with corners.

Abstract: Wind-induced loads and motions play a critical role in designing tall buildings and their lateral structural systems. Building configuration represented by its outer shape is a key parameter in determining these loads and structural responses. However, contemporary architecture trends towards creating taller buildings with more complex geometrical shapes to offer unique designs that become a signature on the map of the world. As a result, evaluating wind-induced motions on such structures becomes more challenging to be evaluated and predicted. This paper presents a computational performance-based aerodynamic optimization with minor imposed modifications that have little to no impact on architectural and structural design intent. The developed tool aims to assist both architects and engineers to seek a sustainable optimal design decision at the early stage of design by employing different computational technological tools in an automated manner. A computational optimization methodology consisting of a computational fluid dynamic coupled with finite element analysis and embedded within a radial basis function surrogate model is proposed to mitigate wind-induced loads on tall buildings. In addition, a numerical example implementing the proposed methodology on selected case study is presented and discussed. The proposed approach was able to achieve a minimization of 13.83% and 23.12% for along-wind and across-wind loads, respectively, which is translated to a reduction in structural response by 12.95% and 14.31% in maximum deflection for along-wind and across-wind directions, respectively.

Abstract: This paper presents a meshless element-free Galerkin method coupled with the radial basis functions (RBFs)-based level set algorithm for topology optimization. The meshless approach provides the structural response and corresponding sensitivities at nodal/grid points, and the solution of RBFs-based level set formulation updates the structural geometry accordingly. Thus, this unique and novel approach allows solution of the optimization problems using a single discretization scheme for both the meshless and the level set methods. A special technique is proposed for the identification of meshless nodal points within the solid and void regions of the structural geometry. The present method handles the appropriate topological modifications, i.e. hole creation, splitting, merging, etc., affectively. Optimal solutions of the benchmark problems suggest reliability and compatibility of the proposed approach versus the mesh-based techniques available within the structural optimization literature.

Abstract: This paper presents a method for simultaneous optimization of the outer shape and internal topology of aircraft wings, with the objective of minimizing drag subject to lift and compliance constraints for multiple load cases. The physics are evaluated by the means of a source-doublet panel method for the aerodynamic response and linear elastic finite elements for the structural response, which are one-way coupled. At each design iteration, a mapping procedure is applied to map the current wing shape and corresponding pressure loads to the unfitted finite element mesh covering the design domain. Wings of small fixed-wing airplanes both with and without a stiffening strut are optimized. The resulting wings show internal topologies with struts and wall-truss combinations, depending on the design freedom of the shape optimization. The lift distributions of the optimized wings show patterns like the ones obtained when performing optimization of wing shapes with constraints on the bending moment at the root.

Abstract: We propose in this paper two kinds of continuity preserving discrete shape gradients of boundary type for PDE-constrained shape optimizations. First, a modified boundary shape gradient formula for shape optimization problems governed by elliptic Dirichlet problems was proposed recently based on the discrete variational outward normal derivatives. The advantages of this new formula over the previous one lie in the improved numerical accuracy and the continuity along the boundary. In the current paper we generalize this new formula to other shape optimization problems including the Laplace and Stokes eigenvalue optimization problems, the shape optimization of Stokes or Navier--Stokes flows, and the interface identification problems. We verify this new formula's numerical accuracy in different shape optimization problems and investigate its performance in several popular shape optimization algorithms. The second contribution of this paper is to propose a continuous discrete shape gradients of boundary type for Neumann problems, by using the ideas of gradient recovery techniques. The continuity property of the discrete boundary shape gradient is helpful in certain shape optimization algorithms and provides certain flexibility compared to the previous discontinuous ones, which are extensively discussed in the current paper.