Singular-ended spline interpolation for two-dimensional boundary element analysis

Abstract

SUMMARYA method of interpolation of the boundary variables that uses spline functions associated with singular elements is presented. This method can be used in boundary element method analysis of 2-D problems that have points where the boundary variables present singular behaviour. Singular-ended splines based on cubic splines and Overhauser splines are developed. The former provides C 2 -continuity and the latter C 1 -continuity across element edges. The potentialities of the methodology are demonstrated analysing the dynamic response of a 2-D rigid footing interacting with a half-space. It is shown that, for a given number of elements at the soil-foundation interface, the singular-ended spline interpolation increases substantially the displacement convergence rate and delivers smoother traction distributions.

Software Development for the Use of Generalized Parabolic Blending in Data Prediction Processes

“…As with the t-dependent change in the r value, the t-dependent change in the s value is also a line equation (Formula 13). 𝒔 = 𝒌𝟑 * 𝒕 + 𝒌𝟒 (13) In Formula 13, the k3 and k4 values must be calculated. If P2 is reachable for the default value (0.5) of s, Formula 14 is obtained.…”

“…Schneider [9] has worked on adding tension to the formula. PB can be applied in boundary conditions [10][11][12][13][14] as Boundary Element Method (BEM). PB has also been an important field of study in the estimation process [18].…”

A quadratic boundary element for 3D elastodynamics

“…Solutions for uniformly-distributed loading cases such as those presented by Romanini et al (2019), however, face a difficult challenge when used to model discontinuous contact problems. Such problems are common in multi-media and multi-body interaction applications, and the challenge is to represent sharply-varying contact tractions that occur at the edges and interfaces between different bodies and media (Barros and Mesquita, 2000). Figure 1 illustrates this problem.…”

“…It shows the horizontal and vertical contact tractions t X and t Z at the interface between a rigid strip footing and a half-space, resulting from the application of an external rocking moment M Y on the footing. These results were computed by Barros and Mesquita (2000) for the normalized frequency of excitation a 0 =ω/c s =1, in which c s is the shear wave speed in the half-space. Modeling quantities like these using uniformly-distributed loading solutions requires large numbers of elements and results in high computational cost, and in some problems is altogether unattainable (Barros and Mesquita, 2009).…”