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Formulation of Problems and Research Techniques in Structural
OneDimensional Optimization Problems
Control by Varying Coefficients
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algorithm anisotropic applied arbitrary attained axis bending boundary conditions boundary curve boundary-value problem calculus of variations coefficients computed condition of Eq conditions for optimality constant thickness constraints of Eq contour control variable corresponding cross-sectional area deflection function denote depend derive determined differential displacement distribution of thickness domain eigenvalue elastic body elastic moduli equation expression formula func function h functional of Eq fundamental frequency given by Eq holes homogeneous homogeneous function inequality of Eq integral isoperimetric condition Lagrange multiplier Lp norm magnitude material maximizing maximum value minimum modulus necessary conditions numerical obtain opti optimal design optimality condition optimization problem optimum distribution optimum shape orthotropy parameter plate Poisson's ratio prob problem of Eqs problems of optimal properties quantities relations respect satisfying Eq side of Eq solve structure Substituting symmetry techniques thickness function tion torsional rigidity trilayer unknown variational principle vector vibration Young's modulus