By Michael A Hicks
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Figure 6 shows the contour plot of the deflection of the plate. (17) where α is the damping factor and Ndof is the total number of degrees of freedom. 3 NUMERICAL SIMULATIONS OF 2D PROBLEMS The plate element presented above has been implemented in a 3D code and coupled with tetrahedral elements for representing the underlying soil. The implementation has been tested for both 2D and 3D cases in which analytical or numerical solutions are available for validation. 1 Cantilever square plate The plate element was first tested for a 2D problem; this being the modelling a square plate, clamped at one end and subjected to a vertical line load at the free end, as shown in Figure 3.
H. 1964, “The particle-in-cell computing method for fluid dynamics’’. Methods for Computational Physics, Vol. (3), 319–343. Lysmer, J. L. 1969, “Finite dynamic model for infinite media’’. Journal of the Engineering Mechanics Division, Vol. (95), 859–877. Sulsky, D. J. L. 1995, “Application of a particle-in-cell method to solid mechanics’’. Computer Physics Communications, Vol. (87), 236–252. Sulsky, D. L. 1996, “Axisymmetric form of the material point method with applications to upsetting and Taylor impact problems’’.
5 m penetration depth. Linear triangular elements were used for the meshes, and 12 material points per element were prescribed on the Gauss integration points initially. Separately a comparison of mesh fineness at contact region was carried out with quadrilateral elements to investigate the influence of rigid contact to the penetration force. Both MPM and DDMP analyses were carried out in these simulations. 2 contact. The maximum shear stresslimit is exactly the cohesion value of the soil. The shear stress concentration starts at the corner of pile tip, and spreads out beneath the soil at about 45°.