Constitutive equations for 0-3 polarized PLZT actuators

AbstractThis article presents constitutive equations of transparent lead lanthanum zirconate titanate (PLZT) materials poling along thickness direction or with 0-3 polarization. Discussed first are the Beer’s law of light transmission in transparent solid and the photovoltaic current density in PLZT materials. Formulas for field strength and electrical potential between two electrodes of a PLZT wafer are then derived from the basic photovoltaic equations. By superposing the photovoltaic and the converse piezoelectric effects, we formulate a novel expression for photo-induced strain that is nonlinearly dependent of incident light intensity and varies with light penetration depth in through-thickness direction. On the basis of the derived photo-induced strain, linear and nonlinear constitutive equations of 0-3 polarized PLZT actuators are formulated. The present model is validated by using the available experimental data in the literature. By using the present model with an exponential variation of strain through the thickness, closed-form solutions for the equivalent loads acting on a PLZT unimorph, bimorph and intelligent beam are obtained and then compared with numerical results available in the literature

A novel algorithm using an orthotropic material model for topology optimization

<p>This article presents a novel algorithm for topology optimization using an orthotropic material model. Based on the virtual work principle, mathematical formulations for effective orthotropic material properties of an element containing two materials are derived. An algorithm is developed for structural topology optimization using four orthotropic material properties, instead of one density or area ratio, in each element as design variables. As an illustrative example, minimum compliance problems for linear and nonlinear structures are solved using the present algorithm in conjunction with the moving iso-surface threshold method. The present numerical results reveal that: (1) chequerboards and single-node connections are not present even without filtering; (2) final topologies do not contain large grey areas even using a unity penalty factor; and (3) the well-known numerical issues caused by low-density material when considering geometric nonlinearity are resolved by eliminating low-density elements in finite element analyses.</p

A New Stress-Based Formulation for Modeling Notched Fiber-Reinforced Laminates

Laminated plates are often modeled with infinite dimensions in terms of the so-called Whitney&ndash;Nuismer (WN) stress criteria, which form a theoretical basis for predicting the residual properties of open-hole structures. Based upon the WN stress criteria, this study derived a new formulation involving finite width; the effects of notch shape and size on the applicability of new formulae and the tensile properties of carbon-fiber-reinforced plastic (CFRP) laminates were investigated via experimental and theoretical analyses. The specimens were prepared by using laminates reinforced by plain woven carbon fiber fabrics and machined with or without an open circular hole or a straight notch. Standard tensile tests were performed and measured using the digital image correlation (DIC) technique, aiming to characterize the full-field surface strain. Continuum damage mechanics (CDMs)-based finite element models were developed to predict the stress concentration factors and failure processes of notched specimens. The characteristic distances in the stress criterion models were calibrated using the experimental results of un-notched and notched specimens, such that the failure of carbon fiber laminates with or without straight notches could be analytically predicted. The experimental results demonstrated well the effectiveness of the present formulations. The new formula provides an effective approach to implementing a finite-width stress criterion for evaluating the tensile properties of notched fiber-reinforced laminates. In addition, the notch size has a great effect on strength prediction while the fiber direction has a great influence on the fracture mode