No abstract

No abstract

No abstract

SUMMARYThis paper develops a ÿnite element scheme to generate the spatial-and time-dependent absorbing boundary conditions for unbounded elastic-wave problems. This scheme ÿrst calculates the spatial-and time-dependent wave speed over the cosine of the direction angle using the Higdon's one-way ÿrst-order boundary operator, and then this operator is used again along the absorbing boundary in order to simulate the behaviour of unbounded problems. Di erent from other methods, the estimation of the wave speed and directions is not necessary in this method, since the wave speed over the cosine of the direction angle is calculated automatically. Two-and three-dimensional numerical simulations indicate that the accuracy of this scheme is acceptable if the ÿnite element analysis is appropriately arranged. Moreover, only the displacements along absorbing boundary nodes need to be set in this method, so the standard ÿnite element method can still be used.

A Hermite differential reproducing kernel (DRK) interpolation-based collocation method is developed for solving fourth-order differential equations where the field variable and its first-order derivatives are regarded as the primary variables. The novelty of this method is that we construct a set of differential reproducing conditions to determine the shape functions of derivatives of the Hermite DRK interpolation, without directly differentiating it. In addition, the shape function of this interpolation at each sampling node is separated into a primitive function possessing Kronecker delta properties and an enrichment function constituting reproducing conditions, so that the nodal interpolation properties are satisfied for the field variable and its first-order derivatives. A weighted least-squares collocation method based on this interpolation is developed for the static analyses of classical beams and plates with fully simple and clamped supports, in which its accuracy and convergence rate are examined, and some guidance for using this method is suggested.