V.E. Verijenko

Developments in thermopiezoelasticity with relevance to smart composite structures

A review of theoretical developments in thermopiezoelasticity having relevance to smart composite structures is presented. The equations governing linear response of piezothermoelastic media are outlined, and a general solution procedure based on potential functions is described. Sensor applications aimed at predicting thermal loads and corresponding responses from measurements of electric potential distributions are described; studies on the control of composite structures (beams, plates and shells) via piezoelectric actuation are reviewed.

Multiobjective optimization of laminated plates for maximum prebuckling, buckling and postbuckling strength using continuous and discrete ply angles

Abstract The optimal design of uniaxially loaded laminated plates subject to elastic in-plane restraints along the unloaded edges are given for a maximum combination of prebuckling stiffness, postbuckling stiffness and buckling load. The results are also obtained for biaxially loaded plates without elastic restraints. The method of solution involves defining a design index comprising a weighted average of the objective functions and identifying candidate configurations which have to be optimized and compared to determine the best stacking sequence. This multiobjective approach leads to improved prebuckling, buckling and postbuckling performance. A similar approach is adopted in the case of discrete ply angles with the provision that these angles can only take predefined values. From a manufacturing viewpoint, using only certain fibre orientations such as 0, ± 45 and 90 ° is advantageous and cost-effective. The multiobjective design results are compared to single objective ones, and the effect of various problem parameters on the optimal designs are numerically studied. It is observed that the resulting trade-off among the different objectives are not severe leading to well-balanced laminates with regard to the range of loads they are required to carry. A comparison of continuous and discrete optimization indicates that both designs lead to comparable load carrying capacity, with regard to different objectives.

Optimum stacking sequence design of symmetric hybrid laminates undergoing free vibrations

The design of hybrid symmetric laminated plates consisting of high-stiffness surface and low-stiffness core layers is presented. The maximisation of the fundamental frequency and frequency separation is performed over a discrete set of available ply angles. Minimum cost design using a hybrid construction is determined subject to a constraint on the fundamental frequencies or frequency separation. Boolean variables are introduced to specify stacking sequences and to obtain an expression for the frequency which is linear in terms of the design variables. Solution of the linear optimisation problem yields an optimal stacking sequence for the specified objective function. The effect of hybridisation is investigated for various parameters of the laminate such as the aspect ratio and the number of plies. Results are given for hybrid graphite-epoxy/glass-epoxy laminates.

Optimization of fiber reinforced composites

A new method for determining the optimal direction and volume fraction of fibers at each point of a structure has been developed. A finite-element discretization is used. The fiber orientation and the fiber volume fraction are assumed to be constant within each element of the model, but they vary from element to element. An algorithm is obtained using variational formulations. It consists of two alternating minimizations: a local one and a global one. The algorithm is shown to be convergent. Results are presented for various laminates subjected to different kinds of edge loads.

Optimization of symmetric laminates for maximum buckling load including the effects of bending-twisting coupling

Finite element solutions are presented for the optimal design of symmetrically laminated rectangular plates subjected to a combination of simply supported, clamped and free boundary conditions. The design objective is the maximization of the biaxial buckling load by determining the fibre orientations optimally, with the effects of bending-twisting coupling taken into account. The finite element method coupled with an optimization routine is employed in analysing and optimizing the laminated plate designs. The effects of boundary conditions, the number of layers and bending-twisting coupling on the optimal ply angles and the buckling load are numerically studied.

Optimal temperature profiles for minimum residual stress in the cure process of polymer composites

Manufacturing of polymer composites using a curing process requires the specification of the temperature as a function of time, i.e., the temperature profile. It is of utmost importance that the selected profile satisfies a number of criteria which include the minimum residual stresses, minimum cure cycle time and full degree of cure. The development of residual stresses during the cure cycle is one of the most important problems as they affect the strength and the mechanical properties of the final product adversely. The object of the present study is to determine the optimal temperature profiles used during curing in order to minimise these stresses. Numerical simulation is used to study the development of stresses during curing based on a process model which includes the effects of chemical and thermal strains and the viscoelastic material behaviour. The process model is implemented to conduct a parametric study to observe the trends and characteristics of the residual stress history varying engineer controllable input parameters. The gradients of the applied temperatures at different dwell times are identified as essential process parameters. An optimised curing cycle based on this observation is developed using the results of the parametric study. The optimal cycle achieves substantial reduction in the residual stresses and curing time for fully cured composites as compared to manufacturer recommended cycles.

Optimal design of hybrid laminates with discrete ply angles for maximum buckling load and minimum cost

The design of hybrid symmetric laminated plates consisting of high-stiffness surface and low-stiffness core layers is presented. In the first problem the maximization of buckling load is carried out over a discrete set of ply angles. In the second problem the minimum number of high-stiffness plies is determined for a given buckling load to minimize the material cost. Boolean variables are introduced to specify stacking sequence. Solution of the linear optimization problem yields an optimal stacking sequence. The effect of hybridization is investigated for various problem parameters such as the aspect ratio of the laminate and the number of plies. The optimal designs are obtained with upper bound constraints on the effect of bending-twisting coupling stiffnesses. Results are given for hybrid graphite-epoxy/glass-epoxy laminates under both uniaxial and biaxial loadings.

Structural analysis of composite lattice shells of revolution on the basis of smearing stiffness

A new approach is developed for analysis of lattice shells of revolution. This approach shows to be more efficient in application to structural analysis and optimisation. Constitutive equations are developed and the expressions for components of stress and strain tensors are derived for the shells of revolution with different lattice patterns. The model for cylindrical lattice shell was realised in a computer code using symbolic computation. Numeric verification of the mathematical models is performed. The advantage of a new homogenisation approach is based on the ability to calculate structural stress resultants without performing finite element analysis which allows to achieve higher computational efficiency. Also this approach allows more design variables to be assigned in the further optimisation analysis.

Optimisation of laminated cylindrical pressure vessels under strength criterion

Abstract An approach for the optimisation of symmetrically laminated cylindrical pressure vessels is presented. The analysis is based on the membrane theory of shells and the optimisation is carried out with respect to the fibre orientations and thickness distributions subject to the Tsai-Wu failure criterion. The approach is equally applicable to balanced and unbalanced symmetrically laminated shells. Two examples are considered which involve the design of cylindrical shells for maximum burst pressure and minimum weight. Numerical results are given for pressure vessels subject to internal pressure only and to a combination of internal pressure and liquid pressure. The effect of axial loading and torque on the designs is discussed.

Stress distribution in continuously heterogeneous thick laminated pressure vessels

Stress analysis of multilayered pressure vessels possessing cylindrical anisotropy and under internal, external and interlaminar pressures is given. The special case when the axis of anisotropy coincides with the axis of symmetry Oz and the stresses do not vary along the generator is investigated. In this case there exists a plane of elastic symmetry normal to this axis at every point of the cylinder so that each layer may be considered as orthotropic. However, elastic properties can vary through the thickness of a layer. Exact elasticity solutions are obtained for both open-ended and closed-ended cylinders using a stress function approach. The method of solution allows the forces on the layer interfaces to be taken into account with relative ease. Numerical results are presented for thick cylinders with isotropic and orthotropic layers, and stress distributions across the thickness are shown.