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SUMMARYA method is presented for minimum weight optimum design of symmetric fibre-composite laminates subject to multiple in-plane loading conditions which takes into account membrane stiffness requirements and strength limitations. The problem is cast as a non-linear mathematical programming problem in which the thicknesses of material placed at preassigned orientation angles are treated as the only design variables. The non-linear programming formulation is transformed into a sequence of linear programs employing an adaptation of the method of inscribed hyperspheres in which only critical and near critical constraints are considered at each stage in the procedure. Example applications illustrate that the method presented offers an efficient and practical optimum design procedure for the fundamental and recurring problem treated.

a b s t r a c tThis paper describes a new approach to optimum weight design of truss structures. The force method is incorporated in an optimization algorithm based on the method of center points. Design variables are the member cross-sectional areas and the redundant forces evaluated for each independent loading condition acting on the structure. The optimization method utilizes the largest hyperspheres inscribed within the feasible space. The method of hyperspheres has been enhanced here to handle the compatibility equality constraints as well. By including the analysis step in the optimization cycle there is no longer the need to perform separate structural analyses thus saving computation time. The viability and efficiency of the proposed method are demonstrated for truss structures subject to multiple loading conditions and constraints on member stresses, nodal displacement and minimum gage. Numerical results are compared with those reported in the literature.

Consideration of surface effects in microscaled and nanoscaled materials is important for accurate prediction of their dynamic behavior. In this study, the Timoshenko beam model is modified to include the surface effects and used to analyze the vibration of nanotubes as well as calculate their natural frequencies. The thin surface layers have been taken into account for rotary inertia computation. Through an example it is shown that dynamic behavior of nanoscaled tubes with consideration of surface effects considerably deviates from the results obtained by classical theories. Plots illustrating such deviations are given to support the conclusions.