Abstract
In this paper, the weak form of bond-associated peridynamic differential operator is proposed to solve differential equations. The presented method inherits the advantages of the original peridynamic differential operator and enables directly and efficiently to determine the nonlocal weak form for local differential equations and obtain the corresponding symmetrical tangent stiffness matrix in the smaller size using variational principles. The concept of bond-associated family is introduced to suppress the numerical oscillation and zero-energy modes in this study. Several typical elasticity problems, taken as examples, are presented to show the application and capabilities of this method. The accuracy, convergence, and stability of the proposed method are demonstrated by seven numerical examples including linear and nonlinear, steady and transient state problems, and eigenvalue problems in 1D, 2D, and 3D cases.