Nonsmooth Mechanics and Convex Optimization

ISBN: 9781138072787 出版年：2011 页码：439 Kanno, Yoshihiro CRC Press

Part I: Convex Optimization Over Symmetric Cone Cones, Complementarity, and Conic Optimization Proper Cones and Conic Inequalities Complementarity over Cones Positive-Semidefinite Cone Second-Order Cone Conic Constraints and Their Relationship Conic Optimization Optimality and Duality Fundamentals of Convex Analysis Optimality and Duality Application to Semidefinite Programming Applications in Structural Engineering Compliance Optimization Eigenvalue Optimization Set-Valued Constitutive Law Part II: Cable Networks: An Example in Nonsmooth Mechanics Principles of Potential Energy for Cable Networks Constitutive law Potential Energy Principles in Convex Optimization Forms More on Cable Networks: Nonlinear Material Law Duality in Cable Networks: Principles of Complementary Energy Duality in Cable Networks (1): Large Strain Duality in Cable Networks (2): Linear Strain Duality in Cable Networks (3): Green-Lagrange Strain Part III: Numerical Methods Algorithms for Conic Optimization Primal-Dual Interior-Point Method Reformulation and Smoothing Method Numerical Analysis of Cable Networks Cable Networks with Pin-Joint Cable Networks with Sliding Joints Form-Finding of Cable Networks Part IV: Problems in Nonsmooth Mechanics Masonry Structures Introduction Principle of Potential Energy for Masonry Structures Principle of Complementary Energy for Masonry Structures Numerical Aspects Planar Membranes Analysis in Small Deformation Principle of Potential Energy for Membranes Principle of Complementary Energy for Membranes Numerical Aspects Frictional Contact Problems Friction Law Incremental Problem Discussions on Various Complementarity Forms Plasticity Fundamentals of Plasticity Perfect Plasticity Plasticity with Isotropic Hardening Plasticity with Kinematic Hardening