The Method of Fundamental Solutions applied to 3D structures with body forces using particular solutions

Abstract

This paper presents the Method of Fundamental Solutions for three-dimensional elastostatics with body forces. The gravitational body loading is considered as an example for the treated body forces. A new set of particular solutions corresponding to such loading is derived using Ho¨rmander operator-decoupling technique, and the relevant particular solution expressions for displacements, tractions and stresses are derived and given explicitly. Several examples are tested and the results confirm the validity and efficiency of the presented method.

Method of fundamental solutions for 3D elasticity with body forces by coupling compactly supported radial basis functions

“…(10) could be a well described function such as gravitational load, for which special particular solution can be found analytically [26]. In many other cases, finding such analytical solution is not a trivial task.…”

A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs

“…We can only give a few examples by mentioning applications to the fields of potential theory, potential flow, and Stokes flow [47,145,278,279,299,302], the biharmonic equation [147], the Helmholtz equation [24], the modified Helmholtz equation [187], elastostatics [76,148,150,196,233], Signorini problems [226], fracture mechanics [124,149], the wave equation and acoustics [12,122,162], heat conduction [43,140,141,143], diffusion 1 [46,133,296,297,300], Stefan problems [44,142], Brinkman flows [275], oscillatory and porous buoyant flow [277], diffusion-reaction equations [22], calculation of eigenfrequencies and eigenmodes [9], radiation and scattering problems [75], acoustic wave scattering on poroelastic scatterers [211], microstrip antenna analysis [252], or to two-dimensional unsteady Burger's equations 2 [298].…”

“…(4.36d) 76 4 Boundary Layer Potentials in Poroelasticity where erf. / is the Gauß error function defined by…”

A multilayer method of fundamental solutions for Stokes flow problems

“…the Laplace, Helmholtz [3], biharmonic [4], and Stokes [5][6][7][8][9][10] equations. However, it can be extended to the solution of more general [2,[11][12][13][14] and inhomogeneous [2,[15][16][17][18][19] equations. It was applied as a straightforward and accurate method to the solution of several engineering problems (e.g.…”

“…It was applied as a straightforward and accurate method to the solution of several engineering problems (e.g. [1,15,[20][21][22][23][24]). Straightforwardness of the implementation and possible exponential convergence are apparent strengths of the MFS.…”