Use of transmitting boundary for loads having non-vanishing time average

Implementation and verification of direct infinite elements in axisymmetric problems

“…In addition, the paper extends previous research (Bakhtaoui and Chelghoum 2020) by comparing results at two control points for a homogeneous axisymmetric model. It further extends this analysis to simulate an axisymmetric bilayer, as presented in the works of Simon & Randolph (1986) or Shridhar & Chandrasekaran (1995). The results of these comparisons confirm the robustness of the proposed method with respect to several dissipative devices commonly used in models subjected to sudden loading.…”

“…The paper revisits the formulation of the method, applied to a direct infinite 4-node element, and emphasises tests conducted to evaluate its performance through an implicit integration scheme in the time domain. These tests include non-vanishing time-averaged loads, reproducing reference dynamic scenarios (Simon & Randolph 1986, Shridhar & Chandrasekaran 1995. In addition, the paper extends previous research (Bakhtaoui and Chelghoum 2020) by comparing results at two control points for a homogeneous axisymmetric model.…”

“…Using Simon and Randolf (1986) and Shridhar and Chandrasekaran (1995) results, the new solution based on a refined mesh (in order to approach the 8 noded elements used by authors), shows also good performance compared to those obtained by viscous boundary and extrapolation algorithm (Figure 7). Used by Shridhar & Chandrasekaran (1995) for validation testing's on the extrapolation algorithm used on the boundaries, this application considers a two-layered medium subjected to the same sudden load applied by a circular area of unit-radius as previously defined. In order to approach the 8 noded elements used by authors, the finite element size is taken as Δx=Δz=0.5, that gives a 60x60 meshing for the reference model.…”

“…The present applications consist in evaluating the response of geological masses with flexible bases, subjected to vertical loads with a non-zero time average. These applications are directly derived from the work of Simons and Randolph (1986), Wolf (1988), Shridhar and Chandrasekaran (1995). The use of these applications makes it possible to test the method by comparing the results obtained with those given in these references.…”

Local transmitting boundaries for the generalized interpolation material point method

“…The simulation for the second problem is carried out using axisymmetric analysis and has previously been used to evaluate the performance of transmitting boundaries in the FEM in the works of Simons and Randolph and Shridhar and Chandrasekaran . Following the aforementioned works,() a background grid of dimensions 9 × 9 m has been used with square elements of size 1.0 m, each containing 4 material points in a 2 × 2 configuration. The material is assumed to be linear elastic with density ρ = 1000 kg/m 3 , shear Modulus G = 1 kPa, and Poisson's ratio υ = 0.25.…”