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# Application developments of mixed finite element method for fluid-structure interaction analysis in maritime engineering

DOI link for Application developments of mixed finite element method for fluid-structure interaction analysis in maritime engineering

Application developments of mixed finite element method for fluid-structure interaction analysis in maritime engineering book

# Application developments of mixed finite element method for fluid-structure interaction analysis in maritime engineering

DOI link for Application developments of mixed finite element method for fluid-structure interaction analysis in maritime engineering

Application developments of mixed finite element method for fluid-structure interaction analysis in maritime engineering book

## ABSTRACT

As shown in Figure 1, a Cartesian coordinate system O − x1x2x3, where the gravitational acceleration is along the negative direction of the coordinate axis O − x3, is chosen as a reference frame to investigate the dynamics of fluid-structure interaction systems. The fluid-solid interaction system consists of a flexible structure of mass density ρs and elastic tensor Eijkl within a domain s of boundary ST ∪ Sw ∪ with its unit normal vector νi and at least one fluid (air or liquid) of sound velocity c in a domain f of boundary f ∪ w ∪ p ∪ with a unit normal vector ηi. The system is excited by external dynamical forces Tˆi, fˆi, pˆ and ground acceleration wˆi. The Cartesian tensors (Fung 1977) with subscripts i, j, k and l (=1, 2, 3) obeying the summation convention

are used in the paper. For example, ui, vi, wi, eij and σij represent displacement, velocity, acceleration vectors, strain and stress tensor in solid, respectively, p denotes the pressure in fluid, ptt = ∂2p/∂t2, ui,j = ∂ui/∂xj , vi = u˙ = ui,t = ∂ui/∂t, wi = v˙i = u¨i = ui,tt = ∂2ui/∂t2, etc. Let us divide this system into Ns substructures in the solid and Nf subdomains in the fluid. A typical substructure represented by Sub(I ), (I = 1, 2, 3, . . . , Ns) has its domain (I )s with displacement boundary S(I )w , traction boundary S

wet interface (Iα) = (αI ) connecting to subdomains Dom(α), α ∈ N (Iα), where N (Iα) denotes a set of ordered numbers of the adjacent subdomains Dom(α), and substructure interfaces S(IJ ) connected to the NI adjacent substructures Sub(J ), (J ∈ N (I )), where N (I ) denotes a set of ordered numbers of the adjacent substructures Sub(J ). Similarly, a typical subdomain represented by Dom(β), (β = 1, 2, 3, . . . , Nf ) has its domain (β)f with boundaries

f ∪(β)w ∪(β)p and f-s coupling interface (βK) = (Kβ) connecting to substructures Sub(K), (K ∈ N (βK)) and subdomain interfaces (βγ ) connected to the nβ adjacent substructures Dom(γ ), (γ ∈ n(β)) where n(β) denotes a set of ordered numbers of the adjacent subdomains Dom(γ ). It is assumed that there exist N independent substructure interfaces, n subdomain interfaces and Nsf fluid-structure interaction interfaces in this division of the system. The governing equations describing the dynamics of the substructures and subdomains are as follows.