000013095 001__ 13095
000013095 005__ 20161114160327.0
000013095 04107 $$aeng
000013095 046__ $$k2009-06-22
000013095 100__ $$aSong, C.
000013095 24500 $$aA high-order polygonal element in structural dynamics

000013095 24630 $$n2.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000013095 260__ $$bNational Technical University of Athens, 2009
000013095 506__ $$arestricted
000013095 520__ $$2eng$$aA high-order polygonal element of arbitrary order and geometry is developed for the dynamic analysis in computational solid mechanics. This polygonal element may have any number and shape of edges as long as a point from which the entire boundary is visible can be identified. Only the boundary is discretized into elements. An edge can also be subdivided into arbitrary number of elements of any order. The inertial effect within the polygon is represented by a high-order mass matrix. No internal mesh is required. The high-order polygonal element is constructed by applying the scaled boundary finiteelement method. An equation for the dynamic stiffness matrix with respect to the degrees of freedom on the boundary is formulated. A continued fraction solution of the dynamic stiffness matrix is obtained recursively. The equation of motion of the polygonal element is formulated by introducing auxiliary variables. A high-order static stiffness matrix and a high-order mass matrix are defined. This polygonal element can also be seamless coupled with standard finite elements when the same shape functions are used on the common edges. A parametric study of the convergence of the solution with increasing order of continued fraction is carried out. Rapid convergence is observed. It is shown that 3-4 terms of continued fraction is sufficient to model one wavelength. Numerical examples demonstrate that the high-order polygonal element of arbitrary order and geometry reduces both the effort in mesh generation and the computer running time.

000013095 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013095 653__ $$aContinued fraction, Higher-order element; Scaled boundary finite-element method, Polygonal element. Abstract. A high-order polygonal element of arbitrary order and geometry is developed for the dynamic analysis in computational solid mechanics. This polygonal element may have any number and shape of edges as long as a point from which the entire boundary is visible can be identified. Only the boundary is discretized into elements. An edge can also be subdivided into arbitrary number of elements of any order. The inertial effect within the polygon is represented by a high-order mass matrix. No internal mesh is required. The high-order polygonal element is constructed by applying the scaled boundary finiteelement method. An equation for the dynamic stiffness matrix with respect to the degrees of freedom on the boundary is formulated. A continued fraction solution of the dynamic stiffness matrix is obtained recursively. The equation of motion of the polygonal element is formulated by introducing auxiliary variables. A high-order static stiffness matrix and a high-order mass matrix are defined. This polygonal element can also be seamless coupled with standard finite elements when the same shape functions are used on the common edges. A parametric study of the convergence of the solution with increasing order of continued fraction is carried out. Rapid convergence is observed. It is shown that 3-4 terms of continued fraction is sufficient to model one wavelength. Numerical examples demonstrate that the high-order polygonal element of arbitrary order and geometry reduces both the effort in mesh generation and the computer running time.

000013095 7112_ $$aCOMPDYN 2009 - 2nd International Thematic Conference$$cIsland of Rhodes (GR)$$d2009-06-22 / 2009-06-24$$gCOMPDYN2009
000013095 720__ $$aSong, C.
000013095 8560_ $$ffischerc@itam.cas.cz
000013095 8564_ $$s513381$$uhttps://invenio.itam.cas.cz/record/13095/files/CD126.pdf$$yOriginal version of the author's contribution as presented on CD, section: Fem: modelling and simulation - i.
000013095 962__ $$r13074
000013095 980__ $$aPAPER