W.M. Vicente

Bi-directional evolutionary structural optimization for design-dependent fluid pressure loading problems

This article presents an evolutionary topology optimization method for compliance minimization of structures under design-dependent pressure loads. In traditional density based topology optimization methods, intermediate values of densities for the solid elements arise along the iterations. Extra boundary parametrization schemes are demanded when these methods are applied to pressure loading problems. An alternative methodology is suggested in this article for handling this type of load. With an extended bi-directional evolutionary structural optimization method associated with a partially coupled fluid–structure formulation, pressure loads are modelled with hydrostatic fluid finite elements. Due to the discrete nature of the method, the problem is solved without any need of pressure load surfaces parametrization. Furthermore, the introduction of a separate fluid domain allows the algorithm to model non-constant pressure fields with Laplaces equation. Three benchmark examples are explored in order to show the achievements of the proposed method.

Topology optimization for submerged buoyant structures

ABSTRACT This paper presents an evolutionary structural topology optimization method for the design of completely submerged buoyant modules with design-dependent fluid pressure loading. This type of structure is used to support offshore rig installation and pipeline transportation at all water depths. The proposed optimization method seeks to identify the buoy design that has the highest stiffness, allowing it to withstand deepwater pressure, uses the least material and has a minimum prescribed buoyancy. Laplaces equation is used to simulate underwater fluid pressure, and a polymer buoyancy module is considered to be linearly elastic. Both domains are solved with the finite element method. Using an extended bi-directional evolutionary structural optimization (BESO) method, the design-dependent pressure loads are modelled in a straightforward manner without any need for pressure surface parametrization. A new buoyancy inequality constraint sets a minimum required buoyancy effect, measured by the joint volume of the structure and its interior voids. Solid elements with low strain energy are iteratively removed from the initial design domain until a certain prescribed volume fraction. A test case is described to validate the optimization problem, and a buoy design problem is used to explore the features of the proposed method.

Minimization of the Effective Thermal Expansion Coefficient of Composite Material Using a Multi-scale Topology Optimization Method

This work proposes a methodology to design composite materials, considering two distinct materials phases and one void phase simultaneously, in order to minimize the thermal expansion coefficients. The design of composite material is treated as a topology optimization problem with a multi-material and multi-scale approach. The Bi-directional Evolutionary Structural Optimization method (BESO) is used to solve the optimization problem and the homogenization method is applied to obtain the equivalent properties for the designed material. In order to show the suitability of the implemented methodology, it is presented one example for the minimization of the homogenized thermal expansion coefficients considering a two-dimensional state of stress. A setting using two material phases, and void was performed resulting in an orthotropic material with thermal expansion less than 10% of the case composing the domain with any of the material phases used.

TOPOLOGY OPTIMIZATION OF PERIODIC STRUCTURES FOR COUPLED ACOUSTIC-STRUCTURE SYSTEMS

Abstract. This work applies the topology optimization technique to an acoustic-structure coupled system with periodic geometry constraint in order to obtain the optimal layout of the design domain for the minimization of the pressure frequency response in the acoustic fluid. The displacement-pressure formulation (u–p) is used for the finite element analysis of the coupled system and external harmonic excitations are applied in the system. The design domain of the coupled system is considered to be composed of identical unit cells. A periodic geometry constraint is applied in the design domain considering the fluid-structure interaction and the objective function. Appling the modified bi-directional evolutionary structural optimization (BESO) technique to the system, the design domain is evolving towards the optimal topology of the unit cells through removing/adding material accordingly to the sensitivity analysis. The influence of the total number of unit cells composing the periodic structure and the aspect ratio of the unit cells are investigated in the minimization of the objective function. In order to show the capability and efficiency of the proposed formulation, two acoustic-structure systems are optimized for several cell configurations, different aspect ratios of the periodic unit cells and excitation frequencies.