Possibilities of the Particle Finite Element Method in computational mechanics

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Abstract

We present some developments in the formulation of the Particle Finite Element Method (PFEM) for analysis of complex coupled problems in fluid and solid mechanics accounting for fluid-structure interaction and coupled thermal effects. The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are viewed as material points which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility of the fluid is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the non linear transient coupled fluid-structure problem is described. Extensions of the PFEM to allow for frictional contact conditions at fluid-solid and solid-solid interfaces via mesh generation are described. A simple algorithm to treat erosion in the fluid bed is presented. Examples of application of the PFEM to solve a number of coupled problems such as the effect of large wave on structures, the large motions of floating and submerged bodies, bed erosion situations and melting and dripping of polymers under the effect of fire are given.