Joaquim Infante Barbosa

A finite element semi-analytical model for laminated axisymmetric shells: statics, dynamics and buckling

Abstract In this paper a numerical method for the structural analysis of laminated axisymmetric shells based on the high-order theory is presented. A higher order displacement field is used with the longitudinal and circumferential components of the displacement given by power series of the transversal coordinate and the condition of zero stress in the top and bottom surfaces of the shell is imposed. In the element formulation the circumferential dependence is carried out by expanding the dependent variables and loading in truncated Fourier series which leads to a semi-analytical element. A special emphasis is given to the coupling effect between the symmetric and anti-symmetric terms for laminated materials with anisotropic properties.

On vibration suppression of magnetostrictive beams

Laminated composite beams containing magnetostrictive layers are modeled as distributed parameter systems and the magnetostrictive layers are used to control the vibration suppression. Velocity feedback with constant gain distributed controller is chosen to achieve vibration suppression. A general formulation of the problem based on classical and shear deformation (the first-order as well as the third-order) theories is presented, and analytical solutions of the equations are developed for simply supported boundary conditions. The effect of material properties, lamination scheme, and placement of the magnetostrictive layers on vibration suppression is investigated.

Sensitivity analysis and optimal design of thin shells of revolution

Thickness and shape design variables are considered. The model is based on a two-node frustum-cone finite element with 8 degrees of freedom based on Love-Kirchhoff assumptions. The objective of the design is the minimization of the volume of the shell material, the minimization of the fundamental natural frequency, the minimization of the maximum stresses, or the minimization of the minimum displacement. The constraint functions are the displacements, stresses, enclosed volume of the structure, volume of shell material or the natural frequency of a specified mode shape. The design sensitivities are calculated analytically, using a symbolic manipulator, semianalytically, and by globally finite difference

The extended unsymmetric frontal solution for multiple-point constraints

Purpose – The purpose of this paper is to discuss the linear solution of equality constrained problems by using the Frontal solution method without explicit assembling. Design/methodology/approach – Re-written frontal solution method with a priori pivot and front sequence. OpenMP parallelization, nearly linear (in elimination and substitution) up to 40 threads. Constraints enforced at the local assembling stage. Findings – When compared with both standard sparse solvers and classical frontal implementations, memory requirements and code size are significantly reduced. Research limitations/implications – Large, non-linear problems with constraints typically make use of the Newton method with Lagrange multipliers. In the context of the solution of problems with large number of constraints, the matrix transformation methods (MTM) are often more cost-effective. The paper presents a complete solution, with topological ordering, for this problem. Practical implications – A complete software package in Fortran 2...

Optimal Design of Piezolaminated Structures Using B-Spline Finite Strip Models and Genetic Algorithms

In this work, a set of numerical models is developed using the B-spline finite strip approach for linear analysis of piezolaminated plates and shells with particular focus to box girder type structures. These models are linked to global optimization techniques, such as genetic algorithms, which may consider either binary or floating point encoding of design variables, along with the inherent particularities of genetic operators at implementation level. Examples are discussed to illustrate the performance of these models.

A Hybrid Procedure to Identify the Optimal Stiffness Coefficients of Elastically Restrained Beams

Abstract The formulation of a bending vibration problem of an elastically restrained Bernoulli-Euler beam carrying a finite number of concentrated elements along its length is presented. In this study, the authors exploit the application of the differential evolution optimization technique to identify the torsional stiffness properties of the elastic supports of a Bernoulli-Euler beam. This hybrid strategy allows the determination of the natural frequencies and mode shapes of continuous beams, taking into account the effect of attached concentrated masses and rotational inertias, followed by a reconciliation step between the theoretical model results and the experimental ones. The proposed optimal identification of the elastic support parameters is computationally demanding if the exact eigenproblem solving is considered. Hence, the use of a Gaussian process regression as a meta-model is addressed. An experimental application is used in order to assess the accuracy of the estimated parameters throughout the comparison of the experimentally obtained natural frequency, from impact tests, and the correspondent computed eigenfrequency.

Shape Optimal Design of Axisymmetric Shell Structures

Structural optimization using finite element techniques requires the sequential use of structural and sensitivity analyses combined with a numerical optimizer. The success of the structural optimization process depends on the proper choices with respect to the finite element model, sensitivity analysis, objective function, constraints, design variables and method of solution of the nonlinear mathematical problem.

Optimal Design of Axisymmetric Shell Structures with Static and Dynamic Constraints

A numerical model is presented for the sensitivity analysis and optimal design of axisymmetric shells. The model is based on a two node frustum conical finite element suitable for axisymmetric plates and shell structures under the action of axisymmetric loading. The design variables are the thicknesses and the objective function is the volume of the material of the structure. The constraints considered are displacements, stresses and natural frequencies. Numerical examples are presented and discussed.

Developments on finite element methods for medical image supported diagnostics

Variational image-processing models offer high-quality processing capabilities for imaging. They have been widely developed and used in the last two decades, enriching the fields of mathematics as well as information science. Mathematically, several tools are needed: energy optimization, regularization, partial differential equations, level set functions, and numerical algorithms. For this work we consider a second-order variational model for solving medical image problems. The aim is to obtain as far as possible fine features of the initial image and identify medical pathologies. The approach consists of constructing a regularized functional and to locally analyse the obtained solution. Some parameters selection is performed at the discrete level in the framework of the finite element method. We present several numerical simulations to test the efficiency of the proposed approach.

Adaptive empirical distributions in the framework of inverse problems

ABSTRACT This article presents an innovative framework regarding an inverse problem. One presents the extension of a global optimization algorithm to estimate not only an optimal set of modeling parameters, but also their optimal distributions. Regarding its characteristics, differential evolution algorithm is used to demonstrate this extension, although other population-based algorithms may be considered. The adaptive empirical distributions algorithm is here introduced for the same purpose. Both schemes rely on the minimization of the dissimilarity between the empirical cumulative distribution functions of two data sets, using a goodness-of-fit test to evaluate their resemblance.