Approximate Solutions to Some Static and Dynamic
نویسنده
چکیده
Problems of optimal structural design for minimum deflection, maximum fundamental frequency and maximum stability are considered in this note. The optimality conditions for these problems consist of nonlinear differential equations which usually require a numerical solution [1-16]. An alternate approach based on the Ritz method is presented here, in which one works with an approximate expression for the objective function rather than the optimality equation. A few examples are considered and some new results are presented. For simplicity the analysis will be restricted to elastic beam-columns subjected to distributed transverse loads and axial loads. Let x be the axial coordinate (0 < x < I), m(x) the mass per unit length and s(;r) the bending stiffness. A sandwich cross-section is assumed, with a linear mass-stiffness relation
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