Finite element developments for general fluid flows with structural interactions

Abstract

SUMMARYThe objective in this paper is to present some developments for the analysis of Navier-Stokes incompressible and compressible fluid flows with structural interactions. The incompressible fluid is discretized with a new solution approach, a flow-condition-based interpolation finite element scheme. The high-speed compressible fluids are solved using standard finite volume methods. The fluids are fully coupled to general structures that can undergo highly non-linear response due to large deformations, inelasticity, contact and temperature. Particular focus is given on the scheme used to couple the fluid media with the structures. The fluids can also be modelled as low-speed compressible or slightly compressible media, which are important models in engineering practice. Some solutions obtained using ADINA are presented to indicate the analyses that can be performed.

A flow‐condition‐based interpolation finite element procedure for triangular grids

“…The trial functions for the perpendicular component h v i⊥ in V h are obtained by replacing x 23 , x 31 and x 12 with Á a , 1 − Á b and b , respectively, and they are the same as the functions used in Equation (8). Note that the bubble function e is not changed as shown in Table III.…”

“…The beneÿt of being able to use rather coarse meshes can be particularly pronounced in the analysis of uid ow structural interactions, because in such analyses, actually, a rather coarse uid ow mesh may well yield su cient accuracy for the tractions on the structure [8]. Here then, in addition to obtaining su cient accuracy in the uid ow prediction, the iterations used to solve the combined nonlinear algebraic equations corresponding to the uid ow and structural meshes should converge fast, and in many cases some Newton-Raphson procedure is best used with consistent Jacobian matrices [9].…”

“…The requirements that we have set for our developments within the FCBI solution approach are [5][6][7][8]10]:…”

“…We concentrate in this paper on the formulation of the proposed discretization scheme, based on the objectives given above, and the detailed solutions of some test problems. Although we consider in this study only steady-state conditions, the proposed method can also be applied to time-dependent problems as is the FCBI method based on quadrilateral grids [8]. Of course, a full evaluation of the scheme should also include a study of its numerical e ciency when the scheme is embedded in a complete CFD computer code.…”

Topology optimization of acoustic–structure interaction problems using a mixed finite element formulation

“…This mixed formulation has previously been suggested for efficient and accurate acoustic-structure interaction analysis [22,23,24]. Our idea to use the mixed formulation in connection with topology optimization comes from previous work on topology optimization of pressure loaded structures [7].…”