Application of Spectral Element Method for Dynamic Analysis of Plane Frame Structures

2019 ◽  
Vol 35 (3) ◽  
pp. 1213-1233 ◽  
Author(s):  
N. Merve Çağlar ◽  
Erdal Şafak
Keyword(s):  
Dynamic Response ◽  
Spectral Element Method ◽  
Computational Cost ◽  
Spectral Element ◽  
Frame Structure ◽  
Frame Structures ◽  
The Finite Element Method ◽  
Plane Frame ◽  
Impedance Functions ◽  
Element Method

The paper presents a methodology to analyze plane frame structures using the Spectral Element Method (SEM) with and without considering Soil-Structure Interaction (SSI). The formulation of spectral element matrices based on higher-order element theories and the assemblage procedure of arbitrarily oriented members are outlined. It is shown that SEM gives more accurate results with much smaller computational cost, especially at high frequencies. Since the formulation is in the frequency domain, the frequency-dependent foundation impedance functions and SSI effects can easily be incorporated in the analysis. As an example, the dynamic response of a plane frame structure is calculated based on the Finite Element Method (FEM) and SEM. FEM and SEM results are compared at different frequency bands, and the effects of SSI on the dynamic response are discussed.

Traffic-induced vibrations of frame structures

2013 ◽  
Vol 40 (2) ◽  
pp. 158-171 ◽  
Author(s):  
Marija Nefovska-Danilovic ◽  
Mira Petronijevic ◽  
Branko Savija
Keyword(s):  
Numerical Simulation ◽  
Numerical Model ◽  
Dynamic Response ◽  
Spectral Element Method ◽  
Structural Models ◽  
Spectral Element ◽  
Frame Structures ◽  
Frame Buildings ◽  
Complex Structural ◽  
Element Method

Using the spectral element method (SEM), a 2-D numerical model of multi-storey frame structures has been developed. The model has been used to predict traffic-induced vibrations of two, six, and twelve-story concrete buildings measured along the route of a future metro line in Belgrade, the capital of Serbia. Vibration simulations of the six-storey frame match satisfactorily the measured dynamic response. However, there is a difference between numerical simulation and the actual measurements for the two-storey and twelve-story buildings. The results indicate a great potential of the proposed SEM to simulate ground-induced vibrations of frame buildings. However, more complex structural models should be developed to better replicate actual situations.

Model reduction strategies for nonlinear beams subjected to large rotary actuations

2009 ◽  
Vol 113 (1150) ◽  
pp. 751-762 ◽  
Author(s):  
B. Stanford ◽  
P. Beran ◽  
M. Kurdi
Keyword(s):  
Spectral Element Method ◽  
Computational Cost ◽  
Elastic Beam ◽  
Spectral Element ◽  
System Of Equations ◽  
Reduced Basis ◽  
Periodic Response ◽  
Time Marching ◽  
Time Periodic ◽  
Element Method

Abstract The solution to nonlinear structural dynamics problems with time marching schemes can be very expensive, particularly if the desired time-periodic response takes many cycles to form. Two cost reduction methods, which need not be considered separately, are formulated in this work. The first projects the nonlinear system of equations onto a reduced basis defined by a set of modes computed with proper orthogonal decomposition. The second utilises a monolithic time spectral element method, whereby the system of ordinary differential equations is converted into a single algebraic system of equations. The spectral element method can be formulated such that only the time-periodic response is computed. These techniques are implemented for a planar elastic beam, actuated at its base to emulate a flapping motion. Nonlinear elastic terms are computed with a corotational finite element method, while inertial terms are computed with a standard multibody dynamics formulation. For a variety of actuation frequencies and kinematic motions, results are given in terms of POD modes, reduced order model accuracy, and computational cost, for both the time marching and the monolithic time schemes.

Mixed Spectral Element Method for 2D Maxwell's Eigenvalue Problem

2015 ◽  
Vol 17 (2) ◽  
pp. 458-486 ◽  
Author(s):  
Na Liu ◽  
Luis Tobón ◽  
Yifa Tang ◽  
Qing Huo Liu
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Higher Order ◽  
The Finite Element Method ◽  
Rigorous Analysis ◽  
Edge Element ◽  
Weak Divergence ◽  
Element Method

AbstractIt is well known that conventional edge elements in solving vector Maxwell's eigenvalue equations by the finite element method will lead to the presence of spurious zero eigenvalues. This problem has been addressed for the first order edge element by Kikuchi by the mixed element method. Inspired by this approach, this paper describes a higher order mixed spectral element method (mixed SEM) for the computation of two-dimensional vector eigenvalue problem of Maxwell's equations. It utilizes Gauss-Lobatto-Legendre (GLL) polynomials as the basis functions in the finite-element framework with a weak divergence condition. It is shown that this method can suppress all spurious zero and nonzero modes and has spectral accuracy. A rigorous analysis of the convergence of the mixed SEM is presented, based on the higher order edge element interpolation error estimates, which fully confirms the robustness of our method. Numerical results are given for homogeneous, inhomogeneous, L-shape, coaxial and dual-inner-conductor cavities to verify the merits of the proposed method.

scholarly journals Application of the Spectral Element Method in a Surface Ship Far-Field UNDEX Problem

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Zhaokuan Lu ◽  
Alan Brown
Keyword(s):  
Information Exchange ◽  
Spectral Element Method ◽  
Computational Cost ◽  
Underwater Explosion ◽  
Structural Response ◽  
Early Time ◽  
Spectral Element ◽  
Far Field ◽  
Surface Ship ◽  
Element Method

The prediction of surface ship response to a far-field underwater explosion (UNDEX) requires the simulation of shock wave propagation in the fluid, cavitation, fluid-structure interaction, and structural response. Effective approaches to model the fluid include cavitating acoustic finite element (CAFE) and cavitating acoustic spectral element (CASE) methods. Although the spectral element method offers the potential for greater accuracy at lower computational cost, it also generates more spurious oscillations around discontinuities which are difficult to avoid in shock-related problems. Thus, the advantage of CASE remains unproven. In this paper, we present a 3D-partitioned FSI framework and investigate the application of CAFE and CASE to a surface ship early-time far-field UNDEX problem to determine which method has the best computational efficiency for this problem. We also associate the accuracy of the structural response with the modeling of cavitation distribution. A further contribution of this work is the examination of different nonmatching mesh information exchange schemes to demonstrate how they affect the structural response and improve the CAFE/CASE methodologies.

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