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B Vibrating discrete structures Vibrating beams
BASIC MATHEMATICAL CONCEPTS WITH ILLUSTRATIONS TAKEN
11 other sections not shown
according to Eq according to theorem active constraints algorithm approximate associated problems assumed assumptions beams column computation concave functions conjugate gradient methods constraint functions contained convergence convex functions convex set corresponding defined in Sect denoted derivatives design variables displacement vector eigenvalue equations example exists expressed feasible region function f fundamental frequency given gj(x gradient method Ineq iteration Kuhn Tucker theorem Lagrange multiplier Lagrangian Let us consider linear space load matrix maximizing maximum minimizing point n-vector non-structural normed space objective function obtained open set optimization problems optimum positive definite positive or zero projection method Proof proved in Sect pseudoconcave quasi-Newton methods quasiconcave Rayleigh quotient respectively satisfies the equality satisfies the inequality scaling line search direction sequence side constraints solution of problem solved space Rn specified statically determinate step length strictly convex subset techniques tends to zero unique solution Vf(x vibration frequencies