Effects of finite element formulation on optimal plate and shell structural topologies (original) (raw)

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.

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

Optimization Of Curved Plated Structures With The Finite Strip And Finite Element Methods

Transactions of the VŠB – Technical University of Ostrava, Civil Engineering Series., 2015

The aim of this study is to compare two available numerical tools for solving of partial differential equations for the optimal design of structures. In the past years numerous methods were developed for topology optimization, from these we have adopted the optimality criteria (OC) approach. The main idea is that we state the optimal conditions, that the minimizer has to fulfil at the end of an iterative proves. This method however is not a general one, only advantageous in the case of separable problems, but comes with fast speed, easy programming, and a relative insensitivity of computational time to the number of variables. In the paper we suggest a new method for the elimination of a numerical error, the so called ‘checkerboard pattern’. In the presented examples we applied one loading case and an elastic material behaviour. The cost function is the net weight of the structure and upper bound of the compliance is set as the optimality constraint.

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

Topology optimization of plate structures using a single- or three-layered artificial material model

Advances in Engineering Software, 2001

This paper presents a topology optimization algorithm for Mindlin±Reissner plate structures. Single-and three-layered arti®cial material models are used with the resizing algorithm of Bendsùe and Kikuchi. The objective is to produce the stiffest single-or three-layered plate for a given volume by redistributing the material throughout the plate. Numerical examples are provided to illustrate the process. q

Formulation and evaluation of a new four-node quadrilateral element for analysis of the shell structures

Engineering with Computers, 2019

Shell structures are lightweight constructions which are extensively used by engineering. Due to this reason presenting an appropriate shell element for analysis of these structures has become an interesting issue in recent decades. This study presents a new rectangular flat shell element called ACM-SQ4 obtained by combining bending and membrane elements. The bending element is a well-known plate bending element called ACM which is based on the classical thin-plate theory and the membrane element is an unsymmetric quadrilateral element called US-Q4θ, the test function of this element is improved by the Allman-type drilling DOFs and a rational stress field is used as the element's trial function. Finally, some numerical benchmark problems are used to evaluate the performance of the proposed flat shell element. The obtained results show that despite its simple formulation, the proposed element has reasonable accuracy and acceptable convergence in comparison with other shell elements.

Formulation, Computation and Application of Optimal Membrane Triangle Element with Drilling Degrees of Freedom

2007

In this study an alternate formulation (optimum membrane triangle (OPT) element that is to reduce the computer programming and the computational cost is presented. The accuracy of finite element program has been established by analyzing some standard benchmarks example. The numerical study indicate that using OPT element for a wide range of aspect ratio, shows the performance with good accuracy in finite element idealization with coarse mesh for analysis of a shear wall structure.

Topology optimization of thin plate structures with bending stress constraints

Computers & Structures, 2016

This paper presents the topology optimization of thin plate structures with bending stress constraints. To avoid the stress singularity phenomena, the qp-relaxation is used for local stress interpolation. The local stress constraints are aggregated into a single global constraint based on the p-norm stress measure. The framework of the topology optimization is constructed using the commercial finite element software ANSYS. In the presented work, the volume of the structure is minimized with the global stress constraint. Numerical examples are demonstrated to validate the proposed topology optimization method.

Topology optimization of load-carryingstructures using three different typesof finite elements

2013

This thesis deals with topology optimization of load-carrying structures, in particular compliance minimization subject to a constraint on the total amount of material to be used. The main purpose of the work was to compare the following three types of finite elements for the above topology optimization problems: Four node square elements with bilinear shape functions, nine node square elements with quadratic shape functions, and six node hexagonal elements with Wachspress shape functions. The SIMP approach (Solid Isotropic Material with Penalization) was used to model the topology optimization problem for different load and support conditions, and the method of moving asymptotes (MMA) was used to solve the formulated optimization problems. On the considered test problems, it turned out that the results obtained by using six node hexagonal elements were in general better than the corresponding results using nine node square elements which in turn were better than the results using f...