José Herskovits

Feasible direction interior-point technique for nonlinear optimization

We propose a feasible direction approach for the minimization by interior-point algorithms of a smooth function under smooth equality and inequality constraints. It consists of the iterative solution in the primal and dual variables of the Karush–Kuhn–Tucker first-order optimality conditions. At each iteration, a descent direction is defined by solving a linear system. In a second stage, the linear system is perturbed so as to deflect the descent direction and obtain a feasible descent direction. A line search is then performed to get a new interior point and ensure global convergence. Based on this approach, first-order, Newton, and quasi-Newton algorithms can be obtained. To introduce the method, we consider first the inequality constrained problem and present a globally convergent basic algorithm. Particular first-order and quasi-Newton versions of this algorithm are also stated. Then, equality constraints are included. This method, which is simple to code, does not require the solution of quadratic programs and it is neither a penalty method nor a barrier method. Several practical applications and numerical results show that our method is strong and efficient.

A two-stage feasible directions algorithm for nonlinear constrained optimization

We present a feasible directions algorithm, based on Lagrangian concepts, for the solution of the nonlinear programming problem with equality and inequality constraints. At each iteration a descent direction is defined; by modifying it, we obtain a feasible descent direction. The line search procedure assures the global convergence of the method and the feasibility of all the iterates.We prove the global convergence of the algorithm and apply it to the solution of some test problems. Although the present version of the algorithm does not include any second-order information, like quasi-Newton methods, these numerical results exhibit a behavior comparable to that of the best methods known at present for nonlinear programming.

An iterative algorithm for limit analysis with nonlinear yield functions

Abstract A mathematical programming algorithm is proposed for the general limit analysis problem. Plastic behavior is described by a set of linear or nonlinear yield functions. Abstract formulations of limit analysis are first considered and a Quasi-Newton strategy for solving the optimality conditions is then sketched. The structure of the problem arising from a finite element discretization is taken into account in order that the algorithm should be able to solve large scale problems.

Active control of axisymmetric shells with piezoelectric layers: a mixed laminated theory with a high order displacement field

This paper presents the development of a semi-analytical axisymmetric shell finite element model with embedded and/or surface bonded piezoelectric ring actuators and/or sensors for active damping vibration control of the structure. A mixed finite element approach is used, which combines the equivalent single-layer higher order shear deformation theory, to represent the mechanical behavior with a layerwise discretization in the thickness direction to represent the distribution of the electric potential of each piezoelectric layer of the frusta conical finite element. To achieve a mechanism of active control of the dynamic response of the structure a feedback control algorithm is used coupling the sensor and active piezoelectric layers. Two illustrative examples are presented and discussed.

Combined numerical-experimental model for the identification of mechanical properties of laminated structures

Abstract A combined numerical–experimental method for the identification of six elastic material modulus of generally thick composite plates is proposed in this paper. This technique can be used in composite plates made of different materials and with general stacking sequences. It makes use of experimental plate response data, corresponding numerical predictions and optimisation techniques. The plate response is a set of natural frequencies of flexural vibration. The numerical model is based on the finite element method using a higher-order displacement field. The model is applied to the identification of the elastic modulus of the plate specimen through optimisation techniques, using analytical sensitivities. The validity, efficiency and potentiality of the proposed technique is discussed through test cases.

Development of a finite element model for the identification of mechanical and piezoelectric properties through gradient optimisation and experimental vibration data

With the increasing use of surface bonded piezoelectric sensors and actuators in laminated structures, rises the need for knowing accurate values for the resulting properties of these structures. The properties obtained through manufacturer data are in most of the cases not enough to predict the structural behaviour and implement efficient control algorithms for active noise and vibration control. To address this issue we propose a discrete finite element model, associated to gradient optimisation and to an inverse method using experimental vibration data to carry out the identification of electromechanical properties in composite plate specimens with surface bonded piezoelectric patches or layers. The properties to be determined are the elastic and piezoelectric constants of the structures constituent materials. 2002 Elsevier Science Ltd. All rights reserved.

A View on Nonlinear Optimization

Once the concepts of a material object are established, the act of designing consists on choosing the values for the quantities that prescribe the object, or dimensioning. These quantities are called Design Variables. A particular value assumed by the design variables defines a configuration. The design must meet Constraints given by physical or others limitations. We have a feasible configuration if all the constraints are satisfied.

A discrete model for the optimal design of thin composite plate-shell type structures using a two-level approach

Abstract The sensitivity analysis of the optimization of general thin shell structures made of composite materials is presented. The model is based on a simple and efficient plate-shell finite element with 18 degress of freedom using the discrete Kirchhoff theory for the bending effects. The design variables consist of the fiber orientation angles and/or thicknesses of each individual layer. The design sensitivities are evaluated through a semi-analytical formulation. The objective of the design is the minimization of a maximum displacement or maximization of a specified natural frequency and the minimization of the volume of plate-shell material which is carried out using a two-level approach. The constraint functions are the displacements, stresses (Tsai-Hill failure criterion), volume of shell material or the natural frequency of a specified vibration mode. Numerical examples are given to show the application, efficiency and accuracy of the proposed model.

Development of semianalytical axisymmetric shell models with embedded sensors and actuators

Abstract This paper presents the development of two semianalytical axisymmetric shell finite element models, which have the possibility of having embedded and/or surface-bonded piezoelectric ring actuators and/or sensors. A mixed finite element approach is used, which combines the equivalent single-layer higher-order shear deformation theory, to represent the mechanical behavior with a layerwise discretization in the thickness direction to represent the distribution of the electrical potential of each piezoelectric layer of the frusta conical finite element. The electrical potential function is represented through a layerwise discretization in the thickness direction and can be assumed linear or quadratic with two or six electrical potential ring nodes per piezoelectric layer. The displacement field and the electrical potential are expanded by Fourier series in the circumferential direction, considering symmetric and anti-symmetric terms. Several examples are presented and discussed to illustrate the accuracy and capabilities of both models.

Damping optimisation of hybrid active-passive sandwich composite structures

Optimisation of active and passive damping is presented in this paper, using a new mixed layerwise finite element model developed for the analysis and optimisation of hybrid active-passive laminated sandwich plates. Optimisation is conducted through maximisation of modal loss factors, using as design variables the viscoelastic core thickness, the constraining elastic layers ply thicknesses and orientation angles, as well as the position of co-located sensor and actuator pairs. Optimal results for passive damping are compared with an alternative optimisation model, based on 3D finite elements included in commercial package ABAQUS. Optimal location for sensor-actuator pairs is also presented and results are discussed.