Pauli Pedersen

Identification of material properties of composite plate specimens

Abstract An indirect identification technique to predict the mechanical properties of composite plate specimens is presented. This technique makes use of experimental eigenfrequencies, the corresponding numerical eigenvalue evaluation, sensitivity analysis and optimization. The laminate analysis is formulated in terms of non-dimensional material parameters and the discrete model is based on the linear shear deformation theory of Mindlin. The constrained minimization of an error functional expressing the difference between measured higher frequencies of a plate specimen and the corresponding numerical ones is then carried out to find the desired optimum parameters. The required sensitivities with respect to changes in the non-dimensional material parameters have the option of being evaluated analytically, semi-analytically or alternatively by finite difference. Results which show the validation of the sensitivities and the limitations of the model to predict the required quantities and its range of application and accuracy are demonstrated through test cases.

Parametrization in laminate design for optimal compliance

Abstract In this paper we consider the maximal stiffness design of laminated plates subjected to single and multiple loads. The stiffness of the laminates are parametrized in terms of the so-called lamination parameters. These express the relation between the material parameters for the laminate and the laminate lay-up and are given as moments of the trigonometric functions that appear in the well-known rotation formulae for stiffness matrices. These relations are here given in a form suitable for optimization studies. The conditions for the laminate itself to be orthotropic are also given directly in terms of the lamination parameters. The design problem is analyzed by performing a reformulation to an equivalent problem which is local in character and it is shown how this, together with an enlargement of the design space to allow for out of plane chattering designs, leads to a significant simplification of the problem. Thus, the number of variables is reduced to only four for the stiffness problem at hand, even in the general case with coupling stiffnesses and multiple loads. Moreover, in the special case of in-plane loads, the optimal solution for each design element of the plate can be realized as a single rotated ply of material or in special strain situations by two plies. A computational solution procedure for the simplified problem is described and several numerical examples illustrate basic features of the design approach.

On the optimal layout of multi-purpose trusses

Abstract This paper provides a solution to the problem of minimum mass design of multi-purpose trusses for which the design variables are not only the areas of the bars but also the positions of the joints. Displacement constraints and non-constant stress constraints (stability) are taken into account. With multiple loading systems, the optimal structure is normally statically indeterminate and generally not even ·fully stressed”. The solution is obtained by successive iterations, using a gradient method with move-limits. For each iteration only the critical forces and displacements are considered and trusses with up to 40 joints have been optimized. Analytical expressions are derived for the necessary gradients, i.e. for the partial derivatives of the displacements and forces with respect to the bar areas and joint coordinates.

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.

Sensitivity analysis for problems of dynamic stability

Abstract In mechanics, as well as in physics, the most general and important thing is to study the dependence of the characteristics of a physical process on problem parameters. Problems of dynamic stability for non-conservative systems involve determination of eigenvalues and eigenvectors. For these problems it is shown in general how the different sensitivity analyses can be performed without any new eigenvalue analyses. The main question relates to the change in flutter load as a function of change in stiffness, mass, boundary conditions, or load distribution. Discretized as well as non-discretized examples are presented in details.

Design with Several Eigenvalue Constraints by Finite Elements and Linear Programming

Abstract A finite element discretization, combined with a powerful numerical eigenvalue procedure, has proved to be a unified approach to eigenvalue analysis of elastic solids. Treating the sensitivity analysis as an integrated part of this approach, one obtains gradients of the eigenvalues without any new eigenvalue analysis. This forms the necessary information for an optimal redesign which is formulated as a linear programming problem. By a sequence of optimal redesigns, one then obtains a solution to the problem of optimal design or a solution to an inverse eigenvalue problem. Taking as an example the vibration of Timoshenko beams, we focus on the gradient functions, on the dependence of slenderness, and on the inherent problem of local optima.

Topology Optimization of Three-Dimensional Trusses

The basic assumption for the present work is the single load condition. In other aspects the stated problem is rather general and the important issue of local stability is taken into account. Even for this problem it is proved that we can always find a statically determined topology that will minimize the cost of the structure. The constraints of the optimization problem are allowable stresses, with thw allowable compressive stresses being design—dependent. The formulation is given in terms of bar forces and a modified Simplex technique is applied for the numerical solution.

Influence of boundary conditions on the stability of a column under non-conservative load

Abstract The cantilever follower force problem with external damping is extended to a three-parameter case, including a concentrated mass, a linear elastic spring, and a partial follower force at the free end. As a result of the study an unexpected, hitherto unrecognized feature of stability/vibration is identified. Normally, the boundary conditions have great influence on the stability limits. However, it is proved that there exists a force at which the critical frequency is independent of all three boundary parameters. The characteristics of this force/frequency combination are discussed in detail, especially in relation to the corresponding eigenfunctions. Also a direct study of the onset of flutter as a function of the boundary parameters is included.

On sufficiency conditions for optimal design based on extremum principles of mechanics

Different results for optimal design can be obtained from the stationarity and extremum principles of mechanics. With focus on second order derivatives, these results are derived and discussed. The important problem of material orientation is then used to exemplify the development, and the similarities arising from working with modulus and compliance matrices are pointed out. For 2D-orthotropic materials an interesting classification is presented.