Dieter Weichert & Alan Ponter 
Limit States of Materials and Structures 
Direct Methods

To predict loading limits for structures and structural elements is one of the oldest and most important tasks of engineers. Among the theoretical and numericalmethodsavailableforthispurpose, so-called“Direct Methods”, – bracing Limit- and Shakedown Analysis, play an eminent role due to the fact that they allow rapid access to the requested information in mathematically constructive manners. The collection of papers in this book is the outcome of a workshop held at Aachen University of Technology in November 2007. The individual c- tributions stem in particular from the areas of new numerical developments renderingthemethodsmoreattractive forindustrialdesign, extensionsofthe general methodology to new horizons of application, probabilistic approaches and concrete technological applications. The papers are arranged according to the order of the presentations in the workshop and give an excellent insight into state-of-the-art developments in this broad and growing ?eld of research. The editors warmly thank all the scientists, who have contributed by their outstanding papers to the quality of this edition. Special thanks go to Jaan Simon for his great help in putting together the manuscript to its ?nal shape.

Table of Content

The Linear Matching Method for Limit Loads, Shakedown Limits and Ratchet Limits.- Large Problems in Numerical Limit Analysis: A Decomposition Approach.- Gurson Model for Porous Pressure Sensitive Materials.- A Direct Method for the Determination of Effective Strength Domains for Periodic Elastic-Plastic Media.- Stochastic Limit Load Analysis of~Elasto-Plastic Plane Frames.- Limit Load Analysis of Plane Frames Under Stochastic Uncertainty.- Reliability Analysis of Inelastic Shell Structures Under Variable Loads.- Static Shakedown Theorem for Solids with Temperature-Dependent Elastic Modulus.- On Shakedown of Structures Under Variable Loads with a Kinematic Non-linear and Non-associated Hardening Rule.- Limit Analysis of Orthotropic Laminates by Linear Matching Method.- Mechanical Surface Treatments and Life Improvement.- Force Method – Based Procedures in the Limit Equilibrium Analysis of Framed Structures.- Shakedown Analysis of Composite Materials Based on Non-linear Mathematical Programming.- A Non-linear Programming Approach to~Shakedown Analysis for a General Yield~Condition.- Application of Shakedown Analysis to Large-Scale Problems with Selective Algorithm.