Propagation of combined longitudinal and torsional stress waves in a functionally graded thin-walled tube

An analytical model for the propagation of combined stress waves in a functionally graded thin-walled tube subjected to combined longitudinal and torsional impact loading is established.The material properties of the tube are assumed to be continuously graded along the length according to a power law function with respect to the volume fractions of the constituents.The generalized characteristic theory is used to analyze the main features of the characteristic wave speeds and simple wave solutions in the functionally graded thin-walled tube.The finite difference method is used to discretize the governing equations.Two types of typical solutions are obtained for the functionally graded tube and the homogeneous tube subjected to combined longitudinal and torsional step loading.The numerical results reveal some abnormal phenomena in the stress path and wave process of the functionally graded thin-walled tube.

A Multi-Domain Boundary Element Method to Analyze the Reflection and Transmission of Oblique Waves From Double Porous Thin Walls

In the present paper, we examine the performance of an efficient type of wave-absorbing porous marine structure under the attack of regular oblique waves by using a Multi-Domain Boundary Element Method(MDBEM). The structure consists of two perforated vertical thin barriers creating what can be called a wave absorbing chamber system. The barriers are surface piercing, thereby eliminating wave overtopping. The problem of the interaction of obliquely incident linear waves upon a pair of perforated barriers is first formulated in the context of linear diffraction theory. The resulting boundary integral equation, which is matched with far-field solutions presented in terms of analytical series with unknown coefficients, as well as the appropriate boundary conditions at the free surface, seabed, and barriers, is then solved numerically using MDBEM. Dissipation of the wave energy due to the presence of the perforated barriers is represented by a simple yet effective relation in terms of the porosity parameter appropriate for thin perforated walls. The results are presented in terms of reflection and transmission coefficients. The effects of the incident wave angles, relative water depths, porosities, depths of the walls, and other major parameters of interest are explored.

EVALUATION OF SINGULAR AND NEARLY SINGULAR INTEGRALS IN THE BEM WITH EXACT GEOMETRICAL REPRESENTATION＊

The geometries of many problems of practical interest are created from circular or ellip- tic arcs. Arc boundary elements can represent these boundaries exactly, and consequently, errors caused by representing such geometries using polynomial shape functions can be removed. To fully utilize the geometry of circular boundary, the non-singular boundary integral equations （BIEs） and a general nonlinear transformation technique available for arc elements are introduced to remove or damp out the singular or nearly singular proper- ties of the integral kernels. Several benchmark 2D elastostatic problems demonstrate that the present algorithm can effectively handle singular and nearly singular integrals occur- ring in the boundary element method （BEM） for boundary layer effect and thin-walled structural problems. Owing to the employment of exact geometrical representation, only a small number of elements need to be divided along the boundary and high accuracy can be achieved without increasing other more computational efforts.