C.A. Mota Soares

Boundary Elements in Shape Optimal Design of Structures

The shape optimal design of shafts and two-dimensional elastic structural components is formulated using boundary elements. The design objective is to maximize torsional rigidity of the shaft or to minimize compliance of the structure, subject to an area constraint. Also a model based on minimum area and stress constraints is developed, in which the real and adjoint structures are identical but have different loading conditions. All degrees of freedom of the models are at the boundary, and there is no need for calculating displacements and stresses in the domain. Formulations based on constant, linear and quadratic boundary elements are developed. A method for accurately calculating the stresses at the boundary is presented, which improves considerably the design sensitivity information. A technique for an automatic mesh refinement of the boundary element models is also developed. The corresponding nonlinear programming problems are solved by Pshenichny’s linearization method. The models are applied to shape optimal design of several shafts and elastic structural components. The advantages and disadvantages of the boundary element method over the finite element techniques for shape optimal design structures are discussed with reference to applications. A literature survey of the development of the boundary element method for shape optimal design is presented.

Finite Element Model for Hybrid Active-Passive Damping Analysis of Anisotropic Laminated Sandwich Structures

In this article, we present a new finite element model for the analyzis of active sandwich laminated plates with a viscoelastic core and laminated anisotropic face layers, as well as piezoelectric sensor and actuator layers. The model is formulated using a mixed layerwise approach, by considering a higher order shear deformation theory to represent the displacement field of the viscoelastic core and a first-order shear deformation theory for the displacement field of the adjacent laminated anisotropic face layers and exterior piezoelectric layers. Control laws are implemented and the model is validated using reference solutions from the literature, and a benchmark application is proposed.

Sensitivity analysis and optimal design of geometrically non-linear laminated plates and shells

Abstract A high order shear deformation theory is used to develop a discrete model for the sensitivity analysis and optimization of laminated plate and shell structures in non-linear response. The geometrically non-linear analysis is based on an updated Lagrangian formulation associated with the Newton–Raphson iterative technique, which incorporates an automatic arc-length procedure. Fiber orientation angles and vectorial distances from middle surface to the upper surface of each layer are considered as the design variables. Different objectives, such as generalized displacements at specified nodes, volume of structural material, and limit load, and constraints of displacement and stress failure criterion are considered. The design sensitivities are evaluated analytically and are compared with sensitivities evaluated by the global finite difference. Numerical examples are given to show the accuracy of the proposed model in the non-linear response and the corresponding design sensitivity analysis, and to show the applicability in the optimal design.

Development of a numerical model for the damage identification on composite plate structures

This paper deals with a numerical technique for the identification of damage on laminated structures. The numerical model is based on a first-order shear deformation finite element. When the structure undergoes some kind of damage, its stiffness is reduced, changing the dynamic response. By considering the sensitivities of the orthogonality conditions of the mode shapes, an algorithm is formulated, which calculates a damage parameter in each finite element. The damage parameter is directly related to the stiffness reduction of the damaged finite element. Only the mechanical properties of the layers of the undamaged plate and the natural frequencies and mode shapes of the damaged plate are required. The proposed numerical model allows the identification of multiple damage and does not require the knowledge of the probable damaged areas. The algorithm is applied to a laminated rectangular plate and its efficiency is demonstrated through several damage simulations.

Higher order models on the eigenfrequency analysis and optimal design of laminated composite structures

Abstract This paper deals with the structural optimization of multilaminated composite plate structures of arbitrary geometry and lay up, using single layer higher order shear deformation theory discrete models. The structural and sensitivity analysis formulation is developed for a family of C 0 Lagrangian elements. The design sensitivities of free vibration response for objective and/or constraint functions with respect to ply angles and ply thickness are presented. The objectives of the design are the maximization of natural frequencies of specified modes and/or the minimization of the structure weight or volume. The accuracy and relative performance of the proposed discrete models are compared and discussed among developed elements and alternative models. Several test designs are optimized to show the applicability of the proposed refined discrete models.

A damage identification numerical model based on the sensitivity of orthogonality conditions and least squares techniques

Abstract This paper presents a numerical model for damage identification of composite structures. This model is based on the orthogonality conditions sensitivities of the damaged and undamaged structure mode shapes and relies on a discretisation by finite elements. The damage is directly related to the stiffness reduction of the damaged element. A study on the use of eigenvector sensitivities for damage identification and the influence of measurement errors and noise in the modal data is also presented. This model is applied to a laminated rectangular plate, free in space, and the efficiency of the numerical tools used to solve the defined set of equations is discussed.

Sensitivity analysis and optimal design of thin laminated composite structures

Abstract In this paper a numerical model for the optimal design of thin plate-shell laminated type structures made of composite materials is presented. The model is based on a plate-shell finite element with 18 degrees of freedom, using the discrete Kirchhoff theory. Sensitivity analysis with respect to fibre orientation and ply thickness is obtained through analytical formulation which is directly included in the finite element code. The model is applied to the optimal design of two test cases.

Buckling sensitivity analysis and optimal design of thin laminated structures

Abstract This paper presents a discrete model for the buckling sensitivity analysis of thin multi-layered angle-ply composite structures. The model is based on a simple and efficient plate-shell element with 18 d.f. using the discrete Kirchhoff theory for the bending effects. Angle-ply design variables and vectorial distances from the middle surface to the upper surface of each layer, indirectly the thickness of each layer, are considered as design variables. The objective of the design is the maximization of the constrained or unconstrained buckling load parameter. The optimization process can be carried out using a two-level approach. The design sensitivities are evaluated analytically, quasi-analytically and by global finite difference. The efficiency and accuracy of the model developed is discussed with reference to several applications.

Analysis of piezolaminated plates by the spline finite strip method

Abstract This paper deals with the development of a family of higher order B-spline finite strip models applied to the static and free vibration analysis of laminated plates, with arbitrary shape and lay-ups, loading and boundary conditions. The lamination scheme can be such that the embedded and/or surface bonded piezoelectric actuating and sensing layers are included. The structure is discretised in a specified number of strips, and the geometry and displacement components of each strip are represented by interpolating functions that are products of linear or cubic B-spline, and linear or quadratic Lagrange functions along the y and x orthonormal directions. The accuracy and relative performance of the proposed discrete models are compared and discussed among the developed and alternative models.

Modelling and design of adaptive structures using B-spline strip models

The aim of this paper is to present a family of laminated plate/shell B-spline finite strip models based on higher order displacement fields applied to the optimal design of laminated composite plate/shell structures with embedded and/or surface bonded piezoelectric actuators and sensors. Simulated annealing, as a stochastic global optimisation technique, is used to improve the performance of composite adaptive structures subjected to behavioural functions and/or constraints, with continuous and discrete design variables. To show the applicability of the proposed optimisation models, two illustrative examples are presented and discussed.