Spectral element method in structural dynamics civil. Rather, this study seeks only to combine the theoretical development of the finite element method with an approach for determining the dynamic structural. Structural mechanics, structural dynamics and stability, theory of elasticity, finite element methods, wave propagation, experimental mechanics. The method combines the flexibility of a finite element method with the accuracy of a spectral method. Triangular spectral element results giraldo, warburton, taylor, a trianglebased spectral element method with diagonal mass matrix, invited paper in preparation for j. It exhibits several favourable computational properties, such as the use of. The second application, a related massspringdamper system, shows how the method can be used to. The prediction of surface ship response to a farfield underwater explosion undex requires the simulation of shock wave propagation in the fluid, cavitation, fluidstructure interaction, and structural response. Application of the spectral element method in a surface. Spectral element method in structural dynamics pdf free download. The spectral element method in structural dynamics. The spectral element method is a highorder finite element technique that combines the geometric flexibility of finite elements with the high accuracy of spectral methods.
In sem, the critical time step is actually smaller due to the non. Spectral element based dynamic large eddy simulation of. Finite element model updating is an alternative to these manual techniques. This method was pioneered in the mid 1980s by anthony patera at mit and yvon maday at parisvi. Wave propagation, diagnostics and control in anisotropic and inhomogeneous structures computational fluid and solid mechanics gopalakrishnan, srinivasan, chakraborty, abir, roy mahapatra, debiprosad on. Using spectral element method for analyzing continuous. Concise analysis of wave propagation using the spectral element method and identification of delamination in cfep composite beams. In a classical finiteelement method, the points that are used to define the. The spectral element model is known to provide very accurate structural dynamic characteristics, while reducing the number of degreeoffreedom to resolve the computational and cost problems. The spectral element method in structural dynamics request pdf. Spectral element method in structural dynamicsspectral element method in structural dynamics usik lee 2009 john wil. Chapter 5 spectral finite element method semantic scholar. Spectral element method in structural dynamics is a concise and timely introduction to the spectral element method sem as a means of solving problems in structural dynamics, wave propagations, and other related fields.
In the numerical solution of partial differential equations, a topic in mathematics, the spectral element method sem is a formulation of the finite element method fem that uses high degree piecewise polynomials as basis functions. The most frequently used in structural dynamics are the finite element method fem and the boundary element method bem. Weak form weak form valid for any test vector boundary conditions automatically included. Finite element model updating for structural applications. One way is to represent the structure member as a single finite element subjected to effective nodal forces and moments at two endnodes of the finite element, which is called the oneelement method oem. The finite element method allows the analysis of complex structural dynamics problems. Spectral integral method and spectral element method domain decomposition method for electromagnetic field analysis by yun lin department of electrical and computer engineering duke university date. Model updating of large structural dynamics models using. Dynamic analysis of smart composite beams by using the. An fftbased spectral element model 31 was used for analysis of. Fe model normally goes through several cycles of manual adjustments. The sem is widely used in computational fluid dynamics and has been succesfully applied to problems in seismology ranging from regional to global scale wave propagation and earthquake dynamics. Spectral integral method and spectral element method.
We present an introduction to the spectral element method, which provides an innovative numerical approach to the calculation of synthetic seismograms in 3d earth models. Optimization of dynamic response using temporal spectral. Haikuo peng 1,3, lin ye 2, guang meng 1, samir mustapha 2 and fucai li 1. Domain partitioned into e highorder quadrilateral or hexahedral elements decomposition may be nonconforming localized refinement trial and test functions represented as n. In the spectral element method sem, there are two ways to deal with external loads applied to a structure member. Thus, the spectral element model for an axially moving bernoullieuler beam subjected to axial tension is developed in the present paper. The spectral element method was introduced in a 1984 paper by a.
They also developed a highly accurate discontinuous sem for time and space fractional advection equation in 38. According to lee spectral element method in structural dynamics, 2009, p. Mark taylor 1 has shown that the spectral element method, a type of fem, is explicitly locally conservative. Concise analysis of wave propagation using the spectral. In essence, it can be considered as a fe method formulated in the frequency domain. We aim to close the gap to the industry by improving the awareness about latest trends in civil engineering.
Next, some direct and iterative methods to solve the resulting linear algebraic systems are. A background,discussion is included that provides a reference to previous works. Research article application of the spectral element method in a. Baynham wessexinstitute of technology,southampton,uk abstract the boundary element method bem is not local and generates a full and nonsymmetric matrix, therefore the matrix solution time could easily grow beyond acceptable limits. Spectral finite element approach for structural dynamics. Themethod the sem was developed more than 15 years ago in computational fluid dynamics 24. The approach employs the timediscontinuous galerkin method and incorporates stabilizing terms having leastsquares form. In the present study we describe a novel threedimensional spectral boundary element algorithm for interfacial dynamics in stokes. Although patera is credited with development of the method, his work was a.
Ge 263 computational geophysics the spectral element method jeanpaul ampuero. Introduction to the spectralelement method sem governing equations equation of motion. Blackburn csiro division of building, construction and engineering. Effective approaches to model the fluid include cavitating acoustic finite element cafe and cavitating acoustic spectral element case methods. A threedimensional spectral boundary element algorithm. Spectral element method in structural dynamics request pdf. These enable a general convergence theorem to be proved in a. Spectral element method in frequency domain is employed to analyze continuous beams and bridges subjected to a moving load. It combines the flexibility of the finiteelement method with the accuracy of the pseudospectral method. Introduction to the spectral element method for three. A by multiplying and combining its rows into a matrix in which the columns consist only.
In the field of structural dynamics, reliable finite element fe response. The spectral element method, sem, is widely used on structural dynamics problems, wave propagation, and other related problems because it allows the accurate description of the dynamic behavior. With this choice the space discretization is similar for both problems. Wave propagation, diagnostics and control in anisotropic and.
Formulated through the femfinite element method because of its use on unstructured grids. The spectral element method combines the accuracy of spectral methods with the geometrical flexibility of finite elements. In the present paper, the methodological framework is the same for the. Before we explain what this method is all about, the. It is shown that the procedure is simplified for a moving load with a constant amplitude and velocity. Modified oneelement method for exact dynamic responses of. To excite or measure the dynamic responses of a laminated composite structure for the active controls of vibrations or noises, wafertype piezoelectric transducers are often bonded on the surface of the composite structure to form a multilayer smart composite structure. Thus, for such smart composite structures, it is very important to develop and use a very reliable mathematical andor. Civilax is the knowledge base covering all disciplines in civil engineering. Solution of movingboundary problems by the spectral. Finite element nonlinear analysis in solid and structural mechanics. In 41, zayernouri and karniadakis developed a spectral and spectral element method for fodes with an exponential accuracy.
This is convenient when solving the equations on a globe. Spectral element method how is spectral element method. Spectral element method in structural dynamics lee, usik on. A petrovgalerkin spectral element method for fractional. The formulation is developed for an euler beam under a moving load with an arbitrary amplitude and velocity. The high accuracy of the spectral element model is then. The main attraction of this approach is that it exploits all the bene. Abstract the spectral element method sem is a high order numerical method for solving partial di. Matlab finite element structural dynamics analysis and engineering applications. Time finite element methods are developed for the equations of structural dynamics.
Finite element model updating involves the solution of a constrained optimization problem. It is demonstrated that a delamination in the composite beam causes the appearance of additional re. Furthermore, in many cases a decoupling between geometry. Reviewgeophysics the spectralelement method, beowulf. Spectral element based dynamic large eddy simulation of turbulent channel flow s. In the spectral element method, as it is understood currently, the idea is to formulate problem in a frequency domain, solve it, and then transform it into. Published 15 july 2010 iop publishing ltd smart materials and structures, volume 19, number 8.
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