Combined shape and reinforcement layout 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.

An integrated approach for shape and topology optimization of shell structures

Computers & Structures, 2002

In this paper an automated approach for simultaneous shape and topology optimization of shell structures is presented. Most research in the last decades considered these optimization techniques separately, seeking an initial optimal material layout and refining the shape of the solution later. The method developed in this work combines both optimization techniques, where the shape of the shell structure and material distribution are optimized simultaneously, with the aim of finding the optimum design that maximizes the stiffness of the shell. This formulation involves a variable ground structure for topology optimization, since the shape of the shell is modified in the course of the process. The method has been implemented into a computational model and the feasibility of the approach is demonstrated using several examples. Ó

Effects of finite element formulation on optimal plate and shell structural topologies

Finite Elements in Analysis and Design, 2009

The effects of selected membrane, plate and flat shell finite element formulations on optimal topologies are numerically investigated. Two different membrane components are considered. The first is a standard 4-node bilinear quadrilateral, and the other is a 4-node element accounting for in-plane (drilling) rotations. Plate elements selected for evaluation include discrete Kirchhoff quadrilateral (DKQ) element as well as two Mindlin-Reissner based elements, one employing selective reduced integration (SRI), and the other an assumed natural strain (ANS) formulation. The flat shell elements consist of an assemblage of these membrane and plate components. Both Mindlin-Reissner elements are shown to recover the thin plate result computed using DKQ elements for popular benchmark topology optimization plate problems. However, a new benchmark problem is introduced illustrating the deficiencies of Mindlin-Reissner elements employing SRI on transverse shear terms. For shell problems, elements which properly account for in-plane rotations are shown to be insensitive to the penalty parameter which enforces the relationship between in-plane rotations and displacements, in contrast to the situation when an ad hoc treatment of drilling degrees of freedom is used.

Optimum Design of Shell Structures with Stiffening Beams

Aiaa Journal, 2004

The optimumdesign of stiffened shell structures is investigated using a robust and ef cient optimizationalgorithm where the total weight of the structure is to be minimized subject to behavioral constraints imposed by structural design codes. Evolutionary algorithms and more speci cally the evolution strategies (ES) method specially tailored for this type of problems is implemented for the solution of the structural optimization problem. The discretization of the stiffened shell is performed by means of cost-effective and reliable shell and beam elements that incorporate the natural mode concept. Three types of design variables are considered: sizing, shape, and topology.A benchmark test example is examined where the ef ciency and robustness of ES over other optimization methods is investigated. Two case studies of stiffened shells are subsequently presented, where a parametric study is undertaken to obtain the most ef cient design compatible with the regulations suggested by design codes such as Eurocode. The important role of the stiffeners and how they can be optimally chosen to improve the performance of shell structures in terms of carrying capacity and economy is demonstrated.

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.

Simultaneous optimization of topology and layout of modular stiffeners on shells and plates

Structural and Multidisciplinary Optimization

Stiffened shells and plates are widely used in engineering. Their performance is highly influenced by the arrangement, or layout, of stiffeners on the base shell or plate and the geometric features, or topology, of these stiffeners. Moreover, modular design is beneficial, since it allows for increased quality control and mass production. In this work, a method is developed that simultaneously optimizes the topology of stiffeners and their layout on a base shell or plate. This is accomplished by introducing a fixed number of modular stiffeners, which are subject to density-based topology optimization and a mapping of these modules to a ground structure. To illustrate potential applications, several stiffened plates and shell examples are presented. All examples demonstrated that the proposed method is able to generate clear topologies for any number of modules and a distinct layout of the stiffeners on the base shell or plate.

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.

Structural optimization strategies for simple and integrally stiffened plates and shells

Engineering Computations, 2005

Purpose – Shells are widely used structural systems in engineering practice. These structures have been used in the civil, automobile and aerospace industries. Many shells are designed using the finite element analysis through the conventional and costly trial and error scheme. As a more efficient alternative, optimization procedures can be used to design economic and safe structures. Design/methodology/approach – This

Structural optimization of stiffened shells using evolutionary algorithms

Computational Fluid and Solid Mechanics 2003, 2003

The optimum design of stiffened shell structures is the main objective of this paper. Combinatorial optimization methods and more specifically algorithms based on evolution strategies are implemented for the solution of the optimization problem. Three optimization types have been considered: sizing, sizing combined with shape and sizing combined with shape and topology. The efficiency of evolution strategies for solving optimization problems of real-scale stiffened shell structures under design codes is examined. For the discretization of the stiffened shell structures the TRIC (TRIangular Composite) and BEC (BEam Composite) elements have been used. TRIC is a simple but sophisticated 3-node sheardeformable isotropic and composite facet shell element suitable for large-scale linear and nonlinear structural behaviour of complex shell structures, while BEC is a 2-node isotropic, composite shear-deformable beam element in space.