Finite element recovery techniques for local quantities of linear problems using fundamental solutions

2003 ◽  
Vol 33 (1) ◽  
pp. 15-21 ◽  
Author(s):  
T. Gr�tsch ◽  
F. Hartmann
Keyword(s):  
Finite Element ◽  
Fundamental Solutions ◽  
Recovery Techniques ◽  
Linear Problems

Nonlinear Finite Element Analysis of Frames Under Interval Material and Load Uncertainty

2015 ◽  
Vol 1 (4) ◽  
Author(s):  
Rafi L. Muhanna ◽  
Robert L. Mullen ◽  
M. V. Rama Rao
Keyword(s):  
Finite Element ◽  
Computational Cost ◽  
Constitutive Models ◽  
Successive Approximations ◽  
Interval Numbers ◽  
Element Analysis ◽  
Geometric Uncertainties ◽  
Secant Stiffness ◽  
Interval Finite Element Method ◽  
Linear Problems

The present study focuses on the development of nonlinear interval finite elements (NIFEM) for beam and frame problems. Three constitutive models have been used in the present study, viz., bilinear, Ramberg–Osgood, and cubic models, to illustrate the development of NIFEM. An interval finite element method (IFEM) has been developed to handle load, material, and geometric uncertainties that are introduced in a form of interval numbers defined by their lower and upper bounds. However, the scope of the previous methods was limited to linear problems. The present work introduces an IFEM formulation for problems involving material nonlinearity under interval material parameters and loads. The algorithm is based on the previously developed high-accuracy interval solutions. An iterative method that generates successive approximations to the secant stiffness is introduced. Examples are presented to illustrate the behavior of the formulation. It is shown that bounding the response of nonlinear structures for a large number of load combinations under uncertain yield stress can be computed at a reasonable computational cost.

A Methodology Based on Structural Finite Element Method-Boundary Element Method and Acoustic Boundary Element Method Models in 2.5D for the Prediction of Reradiated Noise in Railway-Induced Ground-Borne Vibration Problems

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Dhananjay Ghangale ◽  
Aires Colaço ◽  
Pedro Alves Costa ◽  
Robert Arcos
Keyword(s):  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Noise Analysis ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Noise And Vibration ◽  
Model Soil ◽  
Acoustic Bem ◽  
Element Method

This work is focused on the analysis of noise and vibration generated in underground railway tunnels due to train traffic. Specifically, an analysis of noise and vibration generated by train passage in an underground simple tunnel in a homogeneous full-space is presented. In this methodology, a two-and-a-half-dimensional coupled finite element and boundary element method (2.5D FEM-BEM) is used to model soil–structure interaction problems. The noise analysis inside the tunnel is performed using a 2.5D acoustic BEM considering a weak coupling. The method of fundamental solutions (MFS) is used to validate the acoustic BEM methodology. The influence of fastener stiffness on vibration and noise characteristic inside a simple tunnel is investigated.

Hybrid Finite Element Analysis of Heat Conduction in Orthotropic Media with Variable Thermal Conductivities

2020 ◽  
Vol 12 (09) ◽  
pp. 2050098
Author(s):  
Wenkai Qiu ◽  
Keyong Wang ◽  
Peichao Li
Keyword(s):  
Finite Element ◽  
Temperature Field ◽  
Heat Conduction ◽  
Fundamental Solutions ◽  
Element Analysis ◽  
Hybrid Finite Element Method ◽  
Variational Functional ◽  
Hybrid Finite Element ◽  
Element Boundary ◽  
Thermal Conductivities

A hybrid finite element method is proposed for the heat conduction analysis with variable thermal conductivities. A linear combination of fundamental solutions is employed to approximate the intra-element temperature field while standard one-dimensional shape functions are utilized to independently define the frame temperature field along the element boundary. The influence of variable thermal conductivities embeds in the intra-element temperature field via the fundamental solution. A hybrid variational functional, which involves integrals along the element boundary only, is developed to link the two assumed fields to produce the thermal stiffness equation. The advantage of the proposed method lies that the changes in the thermal conductivity are captured inside the element domain. Numerical examples demonstrate the accuracy and efficiency of the proposed method and also the insensitivity to mesh distortion.

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