Modal-Based Finite Elements for Efficient Wave Propagation Analysis

2013 ◽  
Author(s):  
German Capuano ◽  
Massimo Ruzzene ◽  
Julian J. Rimoli
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Finite Elements ◽  
Benchmark Problems ◽  
Fine Scale ◽  
Multi Scale ◽  
Natural Modes ◽  
Propagation Analysis ◽  
Finite Element Formulations

This paper presents an extension to the Geometric Multi-Scale Finite Element Method (GMsFEM) developed by Casadei et al. to predict the dynamic response of heterogeneous materials and structures. The proposed approach introduces elements enriched by the natural modes over their own domain. When heterogeneities are present, the auxiliary fine-scale mesh from GMsFEM is used to calculate the modes numerically. The enrichment scheme is also chosen in such a way that it automatically satisfies continuity across boundaries. The computational efficiency of the method is compared to that of traditional finite element formulations through selected benchmark problems.

HIGHER-ORDER MASS-LUMPED FINITE ELEMENTS FOR THE WAVE EQUATION

2001 ◽  
Vol 09 (02) ◽  
pp. 671-680 ◽  
Author(s):  
W. A. MULDER
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Wave Equation ◽  
Finite Elements ◽  
Finite Difference Method ◽  
Seismic Wave Propagation ◽  
The Finite Element Method ◽  
Efficient Scheme ◽  
The Finite Difference Method

The finite-element method (FEM) with mass lumping is an efficient scheme for modeling seismic wave propagation in the subsurface, especially in the presence of sharp velocity contrasts and rough topography. A number of numerical simulations for triangles are presented to illustrate the strength of the method. A comparison to the finite-difference method shows that the added complexity of the FEM is amply compensated by its superior accuracy, making the FEM the more efficient approach.

scholarly journals MODELLING OF SOIL BEHAVIOR IN DYNAMIC LOAD

2017 ◽  
Vol 13 (3) ◽  
pp. 34-41 ◽  
Author(s):  
Alexander S. Gorodetsky ◽  
Anatol V. Pikul ◽  
Bogdan Y. Pysarevskiy
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Finite Elements ◽  
Half Space ◽  
Dynamic Load ◽  
Dynamic Structure ◽  
Soil Behavior ◽  
Large Size ◽  
Scaled Boundary Finite Element

The paper focuses on simulation of dynamic “structure – soil” interaction and unbounded soil halfspace.Principles for new finite elements developed in LIRA-SAPR software are described. These finite elementssimulate the interaction between bounded domain of soil and the rest part of the half-space. The scaled boundary finite-element method governs these elements. To verify the elements, two problems are solved. The first problem considers the bounded soil where the developed boundary finite elements are introduced. The second problem considers the soil of a relatively large size. Boundary conditions do not influence the wave propagation (conditionally may be treated as unbounded half-space) due to dimensions of soil size. Results differ by 3-8%.

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