Articles in this book examine various materials and how to determine directly the limit state of a structure, in the sense of limit analysis and shakedown analysis. Apart from classical applications in mechanical and civil engineering contexts, the book reports on the emerging field of material design beyond the elastic limit, which has further industrial design and technological applications. Readers will discover that "Direct Methods" and the techniques presented here can in fact be used to numerically estimate the strength of structured materials such as composites or nano-materials, which represent fruitful fields of future applications. Leading researchers outline the latest computational tools and optimization techniques and explore the possibility of obtaining information on the limit state of a structure whose post-elastic loading path and constitutive behavior are not well defined or well known. Readers will discover how Direct Methods allow rapid and direct access to requested information in mathematically constructive manners without cumbersome step-by-step computation. Both researchers already interested or involved in the field and practical engineers who want to have a panorama of modern methods for structural safety assessment will find this book valuable. It provides the reader with the latest developments and a significant amount of references on the topic.

This book provides an overview of direct methods such as limit and shakedown analysis, which are intended to do away with the need for cumbersome step-by-step calculations and determine the loading limits of mechanical structures under monotone, cyclic or variable loading with unknown loading history. The respective contributions demonstrate how tremendous advances in numerical methods, especially in optimization, have contributed to the success of direct methods and their practical applicability to engineering problems in structural mechanics, pavement and general soil mechanics, as well as the design of composite materials. The content reflects the outcomes of the workshop "Direct Methods: Methodological Progress and Engineering Applications," which was offered as a mini-symposium of PCM-CMM 2019, held in Cracow, Poland in September 2019.

This book provides an overview of direct methods such as limit and shakedown analysis, which are intended to do away with the need for cumbersome step-by-step calculations and determine the loading limits of mechanical structures under monotone, cyclic or variable loading with unknown loading history. The respective contributions demonstrate how tremendous advances in numerical methods, especially in optimization, have contributed to the success of direct methods and their practical applicability to engineering problems in structural mechanics, pavement and general soil mechanics, as well as the design of composite materials. The content reflects the outcomes of the workshop "Direct Methods: Methodological Progress and Engineering Applications," which was offered as a mini-symposium of PCM-CMM 2019, held in Cracow, Poland in September 2019.