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# An enrichment technique for bending analysis of in-plane heterogeneous thin plates with weak singularities

**O. Bateniparvar, N. Noormohammadi**

Engineering with Computers

**Abstract**

Static solution of thin elastic plate problems with in-plane varying thickness or material properties having weak point singularities (e.g. crack tip or notches) is studied using a novel enrichment technique. Since the smooth basis functions are not capable of adapting to the adjacency of the singular edge point, enrichment bases called Equilibrated Singular Basis Functions (EqSBFs) are added to improve the solution quality. A combination of Chebyshev polynomials of the first kind and trigonometric functions are used as basis functions. The equilibrium equation is enforced by a weighted residual approach over a fictitious domain which contains the main problem domain. The total integration process is replaced by a composition of normalized pre-evaluated integrals, thus speeding up the procedure considerably. The novelty of the paper is that the proposed method can automatically identify and reproduce the enriching terms corresponding to the singularity order of the problem, which is an advantage with respect to the similar methods that need a priori knowledge of the analytical singularity order. Although the proposed technique is developed in the context of boundary methods, it may also be useful in other enriched methods such as XFEM.