Poroelastodynamics: Linear Models, Analytical Solutions, and Numerical Methods

2009 ◽  
Vol 62 (3) ◽  
Author(s):  
Martin Schanz
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Analytical Solutions ◽  
Linear Models ◽  
Fundamental Solutions ◽  
Numerical Realization ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Element Method

This article presents an overview on poroelastodynamic models and some analytical solutions. A brief summary of Biot’s theory and of other poroelastic dynamic governing equations is given. There is a focus on dynamic formulations, and the quasistatic case is not considered at all. Some analytical solutions for special problems, fundamental solutions, and Green’s functions are discussed. The numerical realization with two different methodologies, namely, the finite element method and the boundary element method, is reviewed.

Transient Stokes Flow in a Wedge

1987 ◽  
Vol 54 (1) ◽  
pp. 203-208 ◽  
Author(s):  
Bohou Xu ◽  
E. B. Hansen
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Boundary Element Method ◽  
Circular Cylinder ◽  
Stokes Flow ◽  
Constant Velocity ◽  
Transient Flow ◽  
The Finite Element Method ◽  
Element Method

The transient flow in the sector region bounded by two intersecting planes and a circular cylinder is determined in the Stokes approximation. The plane boundaries are assumed to be at rest while the cylinder is rotating with a constant velocity starting at t = 0. The problem is solved by means of three different methods, a finite element, a finite difference, and a boundary element method. The corresponding problem in which the constant velocity boundary condition on the cylinder is replaced by a condition of constant stress is also solved by means of the finite element method.

scholarly journals Derivation and optimization of deflection equations for tapered cantilever beams using the finite element method

2020 ◽  
Vol 39 (2) ◽  
pp. 351-362
Author(s):  
M.M. Ufe ◽  
S.N. Apebo ◽  
A.Y. Iorliam
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Cantilever Beam ◽  
Analytical Solutions ◽  
Point Load ◽  
Structural Systems ◽  
The Finite Element Method ◽  
Tapered Cantilever Beam ◽  
Element Method

This study derived analytical solutions for the deflection of a rectangular cross sectional uniformly tapered cantilever beam with varying configurations of width and breadth acting under an end point load. The deflection equations were derived using a numerical analysis method known as the finite element method. The verification of these analytical solutions was done by deterministic optimisation of the equations using the ModelCenter reliability analysis software and the Abaqus finite element modelling and optimisation software. The results obtained show that the best element type for the finite element analysis of a tapered cantilever beam acting under an end point load is the C3D20RH (A 20-node quadratic brick, hybrid element with linear pressure and reduced integration) beam element; it predicted an end displacement of 0.05035 m for the tapered width, constant height cantilever beam which was the closest value to the analytical optimum of 0.05352 m. The little difference in the deflection value accounted for the numerical error which is inevitably present in the analyses of structural systems. It is recommended that detailed and accurate numerical analysis be adopted in the design of complex structural systems in order to ascertain the degree of uncertainty in design. Keywords: Deflection, Finite element method, deterministic optimisation, numerical error, cantilever beam.

scholarly journals Acoustic Noise Computation of Electrical Motors Using the Boundary Element Method

Energies ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 245
Author(s):  
Sabin Sathyan ◽  
Ugur Aydin ◽  
Anouar Belahcen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Finite Element Simulation ◽  
Acoustic Noise ◽  
The Finite Element Method ◽  
Magnetic Forces ◽  
Element Simulation ◽  
Element Method

This paper presents a numerical method and computational results for acoustic noise of electromagnetic origin generated by an induction motor. The computation of noise incorporates three levels of numerical calculation steps, combining both the finite element method and boundary element method. The role of magnetic forces in the production of acoustic noise is established in the paper by showing the magneto-mechanical and vibro-acoustic pathway of energy. The conversion of electrical energy into acoustic energy in an electrical motor through electromagnetic, mechanical, or acoustic platforms is illustrated through numerical computations of magnetic forces, mechanical deformation, and acoustic noise. The magnetic forces were computed through 2D electromagnetic finite element simulation, and the deformation of the stator due to these forces was calculated using 3D structural finite element simulation. Finally, boundary element-based computation was employed to calculate the sound pressure and sound power level in decibels. The use of the boundary element method instead of the finite element method in acoustic computation reduces the computational cost because, unlike finite element analysis, the boundary element approach does not require heavy meshing to model the air surrounding the motor.

scholarly journals Elongation determination using finite element and boundary element method

2015 ◽  
Vol 61 (4) ◽  
pp. 389-394
Author(s):  
Piotr Kisała ◽  
Waldemar Wójcik ◽  
Nurzhigit Smailov ◽  
Aliya Kalizhanova ◽  
Damian Harasim
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Experimental Studies ◽  
Numerical Algorithms ◽  
Mathematical Structure ◽  
The Finite Element Method ◽  
Fbg Sensor ◽  
Element Method

AbstractThis paper presents an application of the finite element method and boundary element method to determine the distribution of the elongation. Computer simulations were performed using the computation of numerical algorithms according to a mathematical structure of the model and taking into account the values of all other elements of the fiber Bragg grating (FBG) sensor. Experimental studies were confirmed by elongation measurement system using one uniform FBG.

Optimization of the Geometry of Shafts Using Boundary Elements

1984 ◽  
Vol 106 (2) ◽  
pp. 199-202 ◽  
Author(s):  
C. A. Mota Soares ◽  
H. C. Rodrigues ◽  
L. M. Oliveira Faria ◽  
E. J. Haug
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Nonlinear Programming ◽  
Boundary Element Method ◽  
Optimal Design ◽  
Boundary Elements ◽  
Linearization Method ◽  
Nonlinear Programming Problem ◽  
The Finite Element Method ◽  
Element Method

The problem of the optimization of the geometry of shafts is formulated in terms of boundary elements. The corresponding nonlinear programming problem is solved by Pshenichny’s Linearization method. The advantages of the boundary element method over the finite element method for optimal design of shafts are discussed, with reference to the applications.

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