An integrated approach for shape and topology optimization of shell structures (original) (raw)

On simultaneous shape and material layout optimization of shell structures

Structural and Multidisciplinary Optimization, 2002

This work presents a computational method for integrated shape and topology optimization of shell structures. Most research in the last decades considered both optimization techniques separately, seeking an initial optimal topology and refining the shape of the solution later. The method implemented in this work uses a combined approach, were the shape of the shell structure and material distribution are optimized simultaneously. This formulation involves a variable ground structure for topology optimization, since the shape of the shell mid-plane is modified in the course of the process. It was considered a simple type of design problem, where the optimization goal is to minimize the compliance with respect to the variables that control the shape, material fraction and orientation, subjected to a constraint on the total volume of material. The topology design problem has been formulated introducing a second rank layered microestructure, where material properties are computed by a “smear-out” procedure. The method has been implemented into a general optimization software called ODESSY, developed at the Institute of Mechanical Engineering in Aalborg. The computational model was tested in several numerical applications to illustrate and validate the approach.

Integrated Shape and Topology Optimization of Cylindrical Shells

The aim of structural optimization is to determine the structural geometry with respect to topology and/or shape of the structures. Thickness/Shape optimization and Topology optimization dealt separately produce improved new designs. However, integration of Thickness/Shape and Topology optimization offer more efficient tool to be used. Depending on the practical considerations in the industry, it is recommended to consider the combination of some vital thickness and shape parameters along with topology optimization. In the present paper an algorithm is formulated integrating shape and topology using a three stage process developed for two objective functions, minimization of structural compliance(maximizing the static stiffness) and maximization of weighted frequency(maximizing the dynamic stiffness). An illustrative example of concrete cylindrical shell is considered from the past researchers (which was optimized only with respect to shape) and using the three stage algorithm optimized models combining shape and topology are obtained for different support conditions. Present work uses ANSYS software and the results are discussed and presented.

Shape Optimization of Shell Structures

International Conference on Aerospace Sciences & Aviation Technology, 2007

This paper deals with structural shape optimisation of prismatic shell structures using genetic algorithm. In the formulation of the optimisation problem, the minimum value of the strain energy is thought as objective function while the volume of each structure remains constant. The optimisation process is carried out for two structures: cylindrical and folded plate structures. The design variables are chosen such that the shape of each studied structure can be represented. The proposed algorithm, used to generate new structural shapes, is linked to a finite element package to calculate the objective function. It is observed that the proposed optimisation algorithm provides an efficient and reliable way of obtaining better solutions for such class of prismatic shell structures.

A hybrid topology optimization algorithm for static and vibrating shell structures

International Journal for Numerical Methods in Engineering, 2002

Structural designers are reconsidering traditional design procedures using structural optimization techniques. Although shape and sizing optimization techniques have facilitated a great improvement in the emergence of new optimum designs, they are still limited by the fact that a suitable topology must be assumed initially. In this paper a hybrid algorithm entitled constrained adaptive topology optimization, or CATO is introduced. The algorithm, based on an artificial material model and an adaptive updating scheme, combines ideas from the mathematically rigorous homogenization (h) methods and the intuitive evolutionary (e) methods. The algorithm is applied to shell structures under static or free vibration situations. For the static situation, the objective is to produce the stiffest structure subject to given loading conditions, boundary conditions and material properties. For the free vibration situation, the objective is to maximize or minimize a chosen frequency. In both cases, a constraint on the structural volume/mass is applied and the optimization process is achieved by redistributing the material through the shell structure. The efficiency of the proposed algorithm is illustrated through several numerical examples of shells under either static or free vibration situations. Copyright © 2002 John Wiley & Sons, Ltd.

Combined shape and reinforcement layout optimization of shell structures

Structural and Multidisciplinary Optimization, 2004

This paper presents a combined shape and reinforcement layout optimization method of shell structures. The approach described in this work is applied to optimize simultaneously the geometry of the shell mid-plane as well as the layout of surface stiffeners on the shell. This formulation involves a variable ground structure, since the shape of the shell surface is modified in the course of the process. Here we shall consider a global structural design criterion, namely the compliance of the structure, following basically the classical problem of distributing a limited amount of material in the most favourable way. The solution to the problem is based on a finite element discretization of the design domain. The material within each of the elements is modelled by a second-rank layered Mindlin plate microstructure. By a simple modification, this type of microstructure can be used to find the optimum distribution of stiffeners on shell structures. The effective stiffness properties are computed analytically through a “smear-out” procedure. The proposed method has been implemented into a general optimization software called Odessy and satisfactorily applied to the solution of some numerical examples, which are illustrated at the end of the paper.

Shape and size optimization of shell structures with variable thickness

2008

paper introduces a methodology for shape and size optimization of shell structures with variable thickness. A model is defined that reduces the number of variables without losing freedom. Several optimization methods are compared. The method of the Coupled Local Minimizers (CLM) offers the certainty of the identification of the global minimum. This methodology is implemented by using MATLAB and ANSYS. It is used successfully for two instructive examples.

Topology optimization of shell structures in architectural design

Architectural Intelligence, 2023

Free-form architectural design has gained significant interest in modern architectural practice. Due to their visually appealing nature and inherent structural efficiency, free-form shells have become increasingly popular in architectural applications. Recently, topology optimization has been extended to shell structures, aiming to generate shell designs with ultimate structural efficiency. However, despite the huge potential of topology optimization to facilitate new design for shells, its architectural applications remain limited due to complexity and lack of clear procedures. This paper presents four design strategies for optimizing free-form shells targeting architectural applications. First, we propose a topology-optimized ribbed shell system to generate free-form rib layouts possessing improved structure performance. A reusable and recyclable formwork system is developed for their effective and sustainable fabrication. Second, we demonstrate that topology optimization can be combined with funicular form-finding techniques to generate a rich variety of elegant designs, offering new design possibilities. Third, we offer cost-effective design solutions using modular components for free-form shells by combining surface planarization and periodic constraint. Finally, we integrate topology optimization with user-defined patterns on free-form shells to facilitate aesthetic expression, exemplified by the Voronoi pattern. The presented strategies can facilitate the usage of topology optimization in shell designs to achieve high-performance and innovative solutions for architectural applications.

Shape Optimization of 3D-Shell Structures Using Simulated Annealing

2000

The goal of this study is to generate global optimum shapes (having the minimum volume or maximum stiffness) for 3D-shell structures subject to given loads and constraints. The constraints may set an upper limit to stresses, displacements or volume. Simulated annealing is used as the optimization algorithm to obtain the optimal design of structural members. Since it is a stochastic algorithm, it requires generation of random configurations. This is achieved by describing the shape of the shell structure through spline curves passing through key points. Whenever the position of a randomly chosen keypoint is changed in a random direction, a new configuration is obtained. A FE structural analysis of these randomly generated configurations is carried out in order to determine the value of the cost function to be minimized. If an improvement is made in the cost, the algorithm accepts the new configuration. But it also allows occasional increases in the cost function to avoid getting stuck into a local minimum point, and thus to converge into the globally minimum point. In this study, by using ANSYS 53 parametric design language, a computer code was developed to build the structures and solve the shape optimization problems. One of the cases considered is presented. The results showed that this method could effectively be applied to the shape optimization of three dimensional shell structures.

Fabrication-aware shape parametrisation for the structural optimisation of shell structures

Engineering Structures

The difficulty to construct mechanically optimal shells may limit the use of structural optimisation in practice. The objective of this paper is to propose a new parametric representation of doubly curved shapes suited for structural optimisation of architectural shells that inherently considers fabrication constraints. We focus on a common construction constraint: the covering of building envelopes with planar facets. This paper proposes to implement the so-called marionette technique as a Computer-Aided-Design tool that guarantees covering of free-form shapes with planar quadrilateral facets. General considerations on the size and nature of the optimisation space created with this method are made. It is demonstrated through different case-studies that the quality of the parametrisation for shape optimisation of shell structures is similar to the one offered by Bézier surfaces, an ubiquitous modelling technique. The proposed method conciliates thus fabrication and structural performance.

Computational Structural Form Finding and Optimization of Shell Structures

Symposium of the International Association For Shell and Spatial Structures Evolution and Trends in Design Analysis and Construction of Shell and Spatial Structures Proceedings, 2010

The purpose of this research is to analyze the structural behaviour of shell structures by studying the way (applied) loads naturally flow through shell structures to their supports and relating this flow off forces to the shell geometry. To unlock this secret will give a fundamental understanding of the behaviour of shell structures and thus the means to design these with form efficiently and elegance. Shells have geometrical and structural properties, which have a close relationship, and determine its structural performance. The newly developed thrust network analysis [1] lays a direct relation in a graphical way between the geometry of a shell and possible funicular solutions under gravity loading, which gives understanding and provides the means for developing new shapes. The "rain flow" analysis [2] makes the relation between the shell geometry and the flow of loads applied to its surface. Similar with the flow of shear forces in plates in bending the "rain flow" analysis gives the relationship between the initial curvatures of the shell surface geometry and the curvatures along the shell's surface which represent the load path of the flow of forces of the shell and the internal forces. By combining these algorithms and analysis methods, a further understanding of the form force relationship of shells can be obtained. This unified approach is the basis for a new computational method for form finding and optimizing shell structures.