P.H. Wen

THE METHOD OF APPROXIMATE PARTICULAR SOLUTIONS FOR SOLVING ELLIPTIC PROBLEMS WITH VARIABLE COEFFICIENTS

A new version of the method of approximate particular solutions (MAPSs) using radial basis functions (RBFs) has been proposed for solving a general class of elliptic partial differential equations. In the solution process, the Laplacian is kept on the left-hand side as a main differential operator. The other terms are moved to the right-hand side and treated as part of the forcing term. In this way, the close-form particular solution is easy to obtain using various RBFs. The numerical scheme of the new MAPSs is simple to implement and yet very accurate. Three numerical examples are given and the results are compared to Kansas method and the method of fundamental solutions.

Cracks in three dimensions : A dynamic dual boundary element analysis

In this paper the dual boundary integral equation for three-dimensional dynamic problems in Laplace space is presented for the first time. The dual boundary element method is used to calculate dynamic stress intensity factors for three-dimensional cracked structures. The application of Laplace transforms to the time-dependent equations of elasticity reduce the problem to a static one in Laplace space. The displacement and traction boundary integral equations for the transformed variables are established by Somiglianas identity. By applying the displacement integral equation on one of the crack surfaces and the traction boundary integral equation on the other, a general mixed-mode crack problem can be solved in a single region, in the same way as a static problem. The transformed mixed-mode stress intensity factors are calculated from the transformed displacement discontinuities near the crack tip. The dynamic stress intensity factors in the time domain are obtained by the use of Durbins inversion method. The accuracy of this method is demonstrated by its application to embedded penny-shaped and elliptical cracks, and edge cracks.

A boundary element method for dynamic plate bending problems

Abstract In this paper the fundamental solution for Kirchhoff plate in the Laplace transform domain is deduced and the boundary element formulation is established to study plate bending problem. By use of the moment integral equation, the dual boundary element equation is developed to solve the cracked plate problem subjected to dynamic loads. Durbin’s Laplace transform inversion method is used and the dynamic stress intensity factors are determined by equivalent stress technique. An infinite plate containing an isolated crack or two cracks, or one set of parallel cracks under Heaviside load on the crack surfaces is studied. The numerical results obtained demonstrate the efficiency and accuracy of the proposed formulation.

A new method for transformation of domain integrals to boundary integrals in boundary element method

In this paper a new technique is presented for transferring the domain integrals in the boundary integral equation method into equivalent boundary integrals. The technique has certain similarities to the dual reciprocity method (DRM) in the way radial basis functions are used to approximate the body force term. However, the resulting integrals are evaluated in a much simpler way. Several examples are presented to demonstrate the validity and accuracy of the proposed paper.

Application of dual reciprocity method to plates and shells

In this paper the dual reciprocity method is developed to transform domain integrals to boundary integrals for shear de-formable plate and shell bending formulation. The force term is approximated by a set of radial basis functions. To transform the domain integrals to boundary integrals using the dual reciprocity method, particular solutions are employed for three radial basis functions. Three examples are presented to demonstrate the accuracy of this method. The numerical results obtained by using different particular solutions are compared with exact and FEM solutions.

Screw Dislocations in a Three-Phase Composite Cylinder Model With Interface Stress

A three-phase composite cylinder model is utilized to study the interaction between screw dislocations and nanoscale inclusions. The stress boundary condition at the interface between nanoscale inclusion and the matrix is modified by incorporating surface/ interface stress. The explicit solution to this problem is derived by means of the complex variable method. The explicit expressions of image forces exerted on screw dislocations are obtained. The mobility and the equilibrium positions of the dislocation near one of the inclusions are discussed. The results show that, compared to the classical solution (without interface stress), more equilibrium positions of the screw dislocation may be available when the dislocation is close to the nanoscale inclusion due to consider interface stress. Also, the mobility of the dislocation in the matrix will become more complex than the classical case.

Boundary element analysis of shear deformable stiffened plates

In this paper a boundary element formulation for analysis of shear deformable stiffened plates is presented. The formulation is derived by coupling boundary element formulation of shear deformable plate and two-dimensional plane stress elasticity. Both concentric and eccentric stiffeners have been considered. The interaction forces between stiffeners and the plate are treated as either line distribution or area distribution of body forces along the attachment. A rectangular stiffened plate and a circular stiffened plate under uniform load are analysed by the proposed method. Good agreement has been achieved compared with other published results.

Boundary element analysis of flat cracked panels with adhesively bonded patches

Abstract Adhesively bonded patch repairs for cracked finite sheets are analysed by the boundary element method. The interaction between the plate and the patch on a repaired sheet is modelled as a distribution of forces which include in-plane, out-of-plane and two moment body forces. The coupled boundary integral formulations of shear deformable plate (Mindlin theory) and two-dimensional plane stress elasticity are presented. Stress intensity factors, three for the bending problem and two for the membrane problem, are evaluated from crack opening displacements. Several examples are presented to demonstrate the accuracy and efficiency of the proposed method. Comparison with two-dimensional solutions demonstrate the significance of the bending loads on the stress intensity factors.

Dual boundary element methods for three-dimensional dynamic crack problems

Abstract In this paper, three formulations of a single-region dual boundary element method for dynamic crack problems are presented. The dynamic stress intensity factors are calculated by crack opening displacement. These methods are developed to study the dynamic behaviour of stationary cracks in threedimensional analysis. Formulations of the methods and computational efficiency characterized by memory and central processing unit time are discussed. In order to compare these three approaches, they are applied to pure mode and mixed-mode crack problems in infinite and finite domains.

Evaluation of mixed-mode stress intensity factors by the mesh-free Galerkin method: Static and dynamic

Based on the variational principle of the potential energy, the element-free Galerkin method is developed using radial basis interpolation functions to evaluate static and dynamic mixed-mode stress intensity factors. For dynamic problems, the Laplace transform technique is used to transform the time domain problem to the frequency domain. The so-called enriched radial basis functions are introduced to capture accurately the singularity of stress at crack tip. In this approach, connectivity of the mesh in the domain or integrations with fundamental or particular solutions are not required. The accuracy and convergence of the mesh-free Galerkin method with enriched radial basis functions for the two-dimensional static and dynamic fracture mechanics are demonstrated through several benchmark examples. Comparisons have been made with benchmarks and solutions obtained by the boundary element method.