Orthogonal meshless finite volume method applied to crack problems

An orthogonal meshless finite volume method has been presented to solve some crack problems. An orthogonal weighted basis function is used to construct shape function so there is not a problem of singularity in this new form. In this work, for three-dimensional fracture problems, a new displacement function is used at the tip of the crack to give a new OMFVM. When the new OMFVM is used, the singularity of the stresses at the tip of the crack can be shown better than that in the primal OMFVM. High computational efficiency and precision are other benefits of the method. Solving some sample crack problems of thin-walled structures show a good performance of this method.

► An orthogonal meshless finite volume method has been presented to solve some crack problems.
► In this work, for three-dimensional fracture problems, a new displacement function is used at the tip of the crack to give a new OMFVM.
► When the new OMFVM is used, the singularity of the stresses at the tip of the crack can be shown better than that in the primal OMFVM.
► High computational efficiency and precision are other benefits of the method.