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.

scholarly journals Structural Damage Detection Using Energy Flow Models

2008 ◽  
Vol 15 (3-4) ◽  
pp. 217-230 ◽  
Author(s):  
E.R.O. Santos ◽  
V.S. Pereira ◽  
J.R.F. Arruda ◽  
J.M.C. Dos Santos
Keyword(s):  
Damage Detection ◽  
Energy Flow ◽  
Structural Damage ◽  
Spectral Element Method ◽  
Crack Nucleation ◽  
Structural Response ◽  
Experimental Tests ◽  
Spectral Element ◽  
Localized Damping ◽  
Element Method

The presence of a crack in a structure modifies the energy dissipation pattern. As a consequence, damaged structures can present high localized damping. Experimental tests have revealed that crack nucleation and growth increase structural damping which makes this phenomenon useful as a damage locator. This paper examines the energy flow patterns caused by localized damping in rods, beams and plates using the Energy Finite Element Method (EFEM), the Spectral Element Method (SEM) and the Energy Spectral Element Method (ESEM) in order to detect and locate damage. The analyses are performed at high frequencies, where any localized structural change has a strong influence in the structural response. Simulated results for damage detection in rods, beams, and their couplings calculated by each method and using the element loss factor variation to model the damage, are presented and compared. Results for a simple thin plate calculated with EFEM are also discussed.

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.

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.

Simulation of anisotropic wave propagation based upon a spectral element method

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1251-1260 ◽  
Author(s):  
Dimitri Komatitsch ◽  
Christophe Barnes ◽  
Jeroen Tromp
Keyword(s):  
Wave Propagation ◽  
Spectral Element Method ◽  
Mass Matrix ◽  
Computational Cost ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Spectral Element ◽  
Weak Formulation ◽  
Element Mesh ◽  
Element Method

We introduce a numerical approach for modeling elastic wave propagation in 2-D and 3-D fully anisotropic media based upon a spectral element method. The technique solves a weak formulation of the wave equation, which is discretized using a high‐order polynomial representation on a finite element mesh. For isotropic media, the spectral element method is known for its high degree of accuracy, its ability to handle complex model geometries, and its low computational cost. We show that the method can be extended to fully anisotropic media. The mass matrix obtained is diagonal by construction, which leads to a very efficient fully explicit solver. We demonstrate the accuracy of the method by comparing it against a known analytical solution for a 2-D transversely isotropic test case, and by comparing its predictions against those based upon a finite difference method for a 2-D heterogeneous, anisotropic medium. We show its generality and its flexibility by modeling wave propagation in a 3-D transversely isotropic medium with a symmetry axis tilted relative to the axes of the grid.

scholarly journals The Implementation of Spectral Element Method in a CAE System for the Solution of Elasticity Problems on Hybrid Curvilinear Meshes

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Dmitriy Konovalov ◽  
Anatoly Vershinin ◽  
Konstantin Zingerman ◽  
Vladimir Levin
Keyword(s):  
Mathematical Simulation ◽  
High Performance ◽  
Spectral Element Method ◽  
New Technologies ◽  
Spectral Element ◽  
High Tech ◽  
Engineering Analysis ◽  
Elasticity Problems ◽  
Cae System ◽  
Element Method

Modern high-performance computing systems allow us to explore and implement new technologies and mathematical modeling algorithms into industrial software systems of engineering analysis. For a long time the finite element method (FEM) was considered as the basic approach to mathematical simulation of elasticity theory problems; it provided the problems solution within an engineering error. However, modern high-tech equipment allows us to implement design solutions with a high enough accuracy, which requires more sophisticated approaches within the mathematical simulation of elasticity problems in industrial packages of engineering analysis. One of such approaches is the spectral element method (SEM). The implementation of SEM in a CAE system for the solution of elasticity problems is considered. An important feature of the proposed variant of SEM implementation is a support of hybrid curvilinear meshes. The main advantages of SEM over the FEM are discussed. The shape functions for different classes of spectral elements are written. Some results of computations are given for model problems that have analytical solutions. The results show the better accuracy of SEM in comparison with FEM for the same meshes.

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