Optimization in Mechanics: Problems and MethodsOptimization in Mechanics: Problems and Methods investigates various problems and methods of optimization in mechanics. The subjects under study range from minimization of masses and stresses or displacements, to maximization of loads, vibration frequencies, and critical speeds of rotating shafts. Comprised of seven chapters, this book begins by presenting examples of optimization problems in mechanics and considering their application, as well as illustrating the usefulness of some optimizations like those of a reinforced shell, a robot, and a booster. The next chapter outlines some of the mathematical concepts that form the framework for optimization methods and techniques and demonstrates their efficiency in yielding relevant results. Subsequent chapters focus on the Kuhn Tucker theorem and duality, with proofs; associated problems and classical numerical methods of mathematical programming, including gradient and conjugate gradient methods; and techniques for dealing with large-scale problems. The book concludes by describing optimizations of discrete or continuous structures subject to dynamical effects. Mass minimization and fundamental eigenvalue problems as well as problems of minimization of some dynamical responses are studied. This monograph is written for students, engineers, scientists, and even self-taught individuals. |
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according to Eq according to theorem algorithms assumed assumptions beams computation concave functions condition constraint functions contained convergence convex functions convex set cross-sectional area denoted derivatives design variables displacement vector eigenvalue elements equations example exists f(x¹ f(x² feasible region function f fundamental frequency given gradient Ineq inequality constraints interval kinematic Kuhn Tucker theorem Lagrange multiplier Lagrangian Let us consider linear space load local minimum locally constrained mass maximizing maximum methods minimizing point minimum n-vector natural vibration non-structural normed space objective function open set optimization problems positive definite positive or zero Proof pseudoconvex quasiconcave quasiconvex Rayleigh quotient respectively saddle point satisfies the equality satisfying the inequality side constraints solution of problem specified statically determinate stress strictly convex subset techniques tends to zero three bars twice differentiable unique solution vibration frequencies