Browsing by Author "Walker, Mark."

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Finite element and analytical solutions for the optimal design of laminated composites.
(1996) Reiss, Talmon.; Adali, Sarp.; Walker, Mark.
The present study involves the analysis and design optimisation of composite structures using analytical and numerical methods. Five different problems are considered. The first problem considers the design of laminated plates subject to non-uniform temperature distributions. The plates are optimised for maximum buckling temperature using the fibre angle as the optimising variable. The method of solution involves the finite element method based on Mindlin theory for thin laminated plates and shells, and numerical optimisation. A computational approach is developed which involves successive stages of solution for temperature distribution, buckling temperature and optimal fibre angle. Three different temperature loadings are considered and various combinations of simply supported and clamped boundary conditions are studied. The effect of plate aspect ratio on the optimal fibre angle and the maximum buckling temperature is investigated. The influence of bending-twisting coupling on the optimum design is studied by considering plates with increasing number of layers. The second problem concerns the optimal design of composite pressure vessels. Finite element solutions are presented for the design of hemispherically and flat capped symmetrically laminated pressure vessels subjected to external pressure. The effect of vessel length, radius and wall thickness, as well as bending-twisting coupling and hybridisation on the optimal ply angle and buckling pressure are numerically studied. Comparisons of the optimal fibre angles and maximum buckling pressures for various vessel geometries are made with those for hybrid pressure vessels. In the third problem, the multiobjective design of a symmetrically laminated shell is obtained with the objectives defined as the maximisation of the axial and torsional buckling loads. The ply angle is taken as the optimising variable and the performance index is formulated as the weighted sum of individual objectives in order to obtain Pareto optimal solutions of the design problem. Single objective design results are obtained and compared with the multiobjective design. The effect of weighting factors on the optimal design is investigated. Results are given illustrating the dependence of the optimal fibre angle and performance index on the cylinder length, radius and wall thickness. In the fourth problem, the optimal layup with least weight or cost for a symmetrically laminated plate subject to a buckling load is determined using a hybrid composite construction. A hybrid construction provides further tailoring capabilities and can meet the weight, cost and strength constraints while a non-hybrid construction may fail to satisfy the design requirements. The objective of the optimisation is to minimise either the weight or cost of the plate using the ply angles, layer thicknesses and material combinations as design variables. As the optimisation problem contains a large number of continuous (ply angles and thicknesses) and discrete (material combinations) design variables, a sequential solution procedure is devised in which the optimal variables are computed in different stages. The proposed design method is illustrated using graphite, kevlar and glass epoxy combinations and the efficiency of the hybrid designs over the non-hybrid ones are computed. Finally, the minimum deflection and weight designs of laminated composite plates are given in the fifth and last problem. The finite element method is used in conjunction with optimisation routines in order to obtain the optimal designs, as was the procedure in the first problem. Various boundary conditions are considered and results are given for varying aspect ratios and for different loading types.
The optimal design of laminated plates for maximum buckling load using finite element and analytical methods.
(1994) Walker, Mark.; Adali, Sarp.; Verijenko, Viktor.
In the first part of the study, finite element solutions are presented for the optimal design of symmetrically laminated rectangular plates subject to a combination of simply supported, clamped and free boundary conditions. The design objective is the maximisation 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 optimisation routine is employed in analysing and optimising the laminated plate designs. The effect of boundary conditions, the number of layers and bending-twisting coupling on the optimal ply angles and the buckling load are numerically studied. Optimal buckling designs of symmetrically laminated rectangular plates under in-plane uniaxial loads which have a nonuniform distribution along the edges are presented in the second part of the study. In particular, point loads, partial uniform loads and nonuniform loads are considered in addition to uniformly distributed in-plane loads which provide the benchmark solutions. Poisson's effect is taken into account when in-plane restraints are present along the unloaded edges. Restraints give rise to in-plane loads at unloaded edges which lead to biaxial loading, and may cause premature instability. The laminate behavior with respect to fiber orientation changes significantly in the presence of Poisson's effect as compared to that of a laminate where this effect is neglected. This change in behavior has significant implications for design optimisation as the optimal values of design variables with or without restraints differ substantially. In the present study, the design objective is the maximisation of the uniaxial buckling load by optimally determining the fiber orientations. Numerical results, determined using the finite element method, are given for a number of boundary conditions and for uniformly and non-uniformly distributed buckling loads. In the third part of the study, finite element solutions are presented for the optimal design of symmetrically laminated rectangular plates with central circular cut-outs subject to a combination of simply supported, clamped and free boundary conditions. The design objective is the maximisation of the biaxial buckling load by determining the fiber orientations optimally. The effect of boundary conditions and bending-twisting coupling on the optimal ply angles and the buckling load are numerically studied. The results are compared to those for laminates without holes. The fourth part of the present study gives optimal designs of symmetrically laminated angle-ply plates, which are obtained with the objective of maximising the initial post buckling stiffness. The design involves optimisation over the ply angles and the stacking sequence to obtain the best laminate configuration. The stacking sequence is chosen from amongst five candidate designs. It is shown that the best configuration depends on the ratio of the in-plane loads in the x and y directions. Results are also given for two additional configurations which do not exhibit bending-twisting coupling. The final section of the present study deals with the optimal design of uniaxially loaded laminated plates subject to elastic in-plane restraints along the unloaded edges for a maximum combination of prebuckling stiffness, postbuckling stiffness and buckling load. This multiobjective study illustrates that improved buckling and post buckling performance can be obtained from plates which are designed in this fashion. The multiobjective results are also compared to single objective design results.