Download e-book for iPad: Coupled Boundary and Finite Element Methods for the Solution by Dr. Siamak Amini, Dr. Paul John Harris, Dr. David T. Wilton

By Dr. Siamak Amini, Dr. Paul John Harris, Dr. David T. Wilton (auth.)

This textual content considers the matter of the dynamic fluid-structure interplay among a finite elastic constitution and the acoustic box in an unbounded fluid-filled external area. the outside acoustic box is modelled via a boundary imperative equation over the constitution floor. in spite of the fact that, the classical boundary fundamental equation formulations of this challenge both don't have any ideas or wouldn't have distinct suggestions at convinced attribute frequencies (which depend upon the skin geometry) and it will be important to hire transformed boundary imperative equation formulations that are legitimate for all frequencies. the actual method followed right here consists of an arbitrary coupling parameter and the influence that this parameter has at the balance and accuracy of the numerical procedure used to resolve the quintessential equation is tested. The boundary critical research of the outside acoustic challenge is coupled with a finite point research of the elastic constitution with the intention to examine the interplay among the dynamic behaviour of the constitution and the linked acoustic box. lately there was a few controversy over even if the coupled challenge additionally suffers from the non-uniqueness difficulties linked to the classical essential equation formulations of the outside acoustic challenge. this query is resolved via demonstrating that .the strategy to the coupled challenge isn't particular on the attribute frequencies and that it is crucial to hire an fundamental equation formula legitimate for all frequencies.

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Extra resources for Coupled Boundary and Finite Element Methods for the Solution of the Dynamic Fluid-Structure Interaction Problem

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2 respectively. This ensures that the normal to Sj is directed into D+. 1: The relationship between the nodes of a general linear element and those of the reference element. 2: The relationship between the nodes of a general quadratic element and those of the reference element. The interpolation, or basis, functions are defined to be unity at one node and zero at all the others. The basis functions for the linear element are Nl =1- u - V N2 =U N3 = v. 61) The basis functions for the quadratic element are Nl = (1 - u - v)(1 - 2u - 2v) N2 = 4u(1- u - v) N3 = u(2u - 1) N 4 =4uv N5=V(2v-1) N 6 =4v(1-u-v).

29). 2 the singularity will occur at n,~) in the (u,v) plane. 71)) is applied to each sub-triangle, where (U1' vt}, (U2' V2) and (U3, V3) are the vertices of the sub-triangle and (U1,Vt} = (~, ~). 75) i=1 with similar expressions for Yq - YP and Zq - zp and where m = 3 or 6 is the number of nodes in the element. 76) is zero if and only if S = o. It is easy to show that Ni ( u, v) can be written in the form Ni(u, v) and hence = Ni(Ull vt} + sNi(s, t) i = 1,2, ... 77) m Xq - xp = LXi[Ni(U1, vt} + sNi(s, t)]- xp i=1m = sLNi(s,t)Xi.

26) The n collocation points {Pll P2, ... 2. 17) and collocating at the points Pi yields the linear system ->'4>i + f4>j j=1 1 Sj k(pi' q)dSq = f(Pi) = 1,2, ... 28) for 4>1l 4>2, ... ,4>n. 29) p,qES, 1 denote the maximum of the sub-region diameters. 30) where c is a constant, see [13J. 31) = O(h). Using this collocation scheme the matrix approximations to the layer potential operators Lk, Mk and Ml are given by 1 (M ) .. 32) Gk(Pi, q)dSq Sj 8Gk(Pi , q) dS Sj 1 s. 34) respectively. It should be noted that the matrix Ml is not the transpose of the matrix Mk • If i = j the integrands of all three integrals are weakly singular and care must be 30 taken in evaluating them.

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