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A complex variable meshless method for fracture problems. (English) Zbl 1147.74410
Summary: Based on the moving least-square (MLS) approximation, the complex variable moving least-square approximation (CVMLS) is discussed in this paper. The complex variable moving least-square approximation cannot form ill-conditioned equations, and has greater precision and computational efficiency. Using the analytical solution near the tip of a crack, the trial functions in the complex variable moving least-square approximation are extended, and the corresponding approximation function is obtained. And from the minimum potential energy principle, a complex variable meshless method for fracture problems is presented, and the formulae of the complex variable meshless method are obtained. The complex variable meshless method in this paper has greater precision and computational efficiency than the conventional meshless method. Some examples are given.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
74Rxx Fracture and damage
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