Here the element-free Galerkin (EFG) method is applied to limit analysis problems. It is therefore worthwhile exploring a range of alternative methods. However, when finite elements are used, the solutions obtained can be highly sensitive to the geometry of the original mesh, particularly in the region of stress or displacement singularities. Numerical procedures based on the finite element method (FEM) are particularly well-established. This places demands on the numerical discretisation strategy adopted, as well as on the mathematical programming tools applied. Current research in the field of limit analysis is focussed on the development of numerical tools which are sufficiently efficient and robust to be used in engineering practice. Difficulties in performing incremental-iterative elasto-plastic analyses have motivated the development of numerical variants of classical 'limit analysis' methods, in which the limit load is identified directly. Limit state techniques are used to design and assess the safety of engineering components and structures.
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