Limit analysis can be used to directly calculate the ultimate load of structures without considering cumbersome elastic–plastic analysis. We present an adaptive mesh refinement strategy by mean of extended isogeometric analysis (XIGA) in association with second-order cone programming (SOCP) for kinematic limit analysis of hole and inclusion problems. The location of hole and inclusion can be captured by level set function without regard for its interfaces. The local refined non-uniform rational B-splines (LR NURBS), allowing local refinement and modeling complex geometries, are selected as basis functions. The structured mesh refinement strategy is exploited to carry out local refinement on the basis of the indicator of -norm of plastic strain rates. The adaptive local refinement can detect the local plastic deformation regions, and further reveals the possible failure mechanisms. The discrete kinematic formulation of limit analysis can be rewritten as the form of SOCP, and further is solved efficiently with the help of the Mosek toolbox. All the desirable features of the present approach are illustrated through numerical experiments.
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