Recent Advances in Boundary Element Methods and their Solid Mechanics Applications
July 2, 2001 — July 6, 2001
- Dimitri E. Beskos (University of Patras, Patras, Greece)
During the last 30 years or so, Boundary Element Methods (BEM) have been developed and successfully applied to the solution of a variety of engineering problems. BEM are at their best when applied to linear static or dynamic problems. However, during the last 15 years or so, BEM have also been successfully applied to the solution of a variety of materially and geometrically nonlinear problems. When non-linearities are present, the BEM loose their dimensionality reduction advantage over Finite Element Methods (FEM) since an interior discretization is necessary in addition to the boundary one. However, some advantages of BEM over FEM are still present.
This course presents and discusses recent advances in BEM and their solid mechanics applications in those areas where these numerical methods prove to be the ideal solution tool. The aim is to illustrate the methods in the most recent forms (developed during the last 5–10 years) and demonstrate their advantages for a wide variety of solid mechanics problems.
The solid mechanics areas which have received special attention by researchers in the field during the last 5–10 years and which are considered in this course are the following: 1) Special formulations and accurate and efficient numerical treatment of BEM, including symmetric formulations and computation of singular and hypersingular integrals. 2) Efficient treatment of materially and geometrically nonlinear static and dynamic problems, including inelastic (elastoplastic, viscoplastic, damage) behaviour, unilateral contact analysis and inelastic fracture mechanics. 3) Application to large static and dynamic problems of structural system analysis, including large three-dimensional systems, plates and shells and soil &endash; structure interaction. 4) Application to various structural shape optimization and inverse or identification problems under both static and dynamic conditions, which are important in optimum structural design and nondestructive evaluation techniques. All the above categories of problems are presented in this course by specialists in the field.
The course is addressed to postgraduate students, academics, research and practicing engineers interested in numerical methods, especially BEM, for the analysis of solids and structures.