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.

A Hybrid Finite Element Method for Calculating the Vibration of Co-Linear Beams in the Mid-Frequency Range

1999 ◽  
Author(s):  
Xi Zhao ◽  
Nickolas Vlahopoulos
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Theoretical Development ◽  
Frequency Range ◽  
Element Analysis ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element ◽  
New Formulation ◽  
Element Method

Abstract The theoretical development of a hybrid finite element method is presented. It combines conventional Finite Element Analysis (FEA) with Energy Finite Element Analysis (EFEA) in order to achieve a numerical solution to mid-frequency vibrations. In the mid-frequency range a system is comprised by some members that contain several wavelengths and some members that contain a small number of wavelengths. The former are considered long members and they are modeled by the EFEA. The latter are considered short and they are modeled by the FEA. The new formulation is based on deriving appropriate interface conditions at the joints between sections modeled by the EFEA and the FEA methods. Since the work presented in this paper constitutes a fundamental step in the development of a hybrid method for mid-frequency analysis, the formulation for one flexural degree of freedom in co-linear beams is presented. The excitation is considered to be applied on a long member and the response of the entire system is computed. Uncertainty effects are imposed only on the long members of the system. Validation cases for several configurations are presented.

Brain Tissue Fragility–A Finite Strain Analysis by a Hybrid Finite-Element Method

1975 ◽  
Vol 42 (2) ◽  
pp. 269-273 ◽  
Author(s):  
S. N. Atluri ◽  
A. S. Kobayashi ◽  
J. S. Cheng
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Finite Strain ◽  
Strain Analysis ◽  
Stress And Strain ◽  
Exposed Surface ◽  
Element Analysis ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element

This paper deals with the finite-strain, finite-element analysis of the states of stress and strain in the vicinity of a blunt indenter applied to the exposed surface of the pia-arachnoid of an anesthetized rhesus monkey.

Thermal stress analysis of plates and shallow shells by hybrid finite-element method

1974 ◽  
Vol 9 (3) ◽  
pp. 152-158
Author(s):  
B Tabarrok ◽  
V S Hoa
Keyword(s):  
Finite Element ◽  
Thermal Stress ◽  
Stress Analysis ◽  
Element Model ◽  
Displacement Fields ◽  
Shallow Shells ◽  
Thermal Stress Analysis ◽  
Hybrid Finite Element Method ◽  
Variational Functional ◽  
Hybrid Finite Element

A rectangular finite-element model has been developed for thermal-stress analysis of shallow shells. The elemental equations are obtained from a two-field variational principle which employs equilibriating stress fields within the elements and compatible displacement fields along inter-element boundaries. The extremization of the variational functional tends to satisfy the compatibility requirements within the elements and equilibrium conditions along inter-element boundaries. The element is employed for thermal-stress analysis of several examples and the numerical results obtained are compared with some analytical results.

A Hybrid Finite Element Formulation for Mid-Frequency Analysis of Systems With Excitation Applied on Short Members

2000 ◽  
Author(s):  
Xi Zhao ◽  
Nickolas Vlahopoulos
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Input Power ◽  
Element Formulation ◽  
Element Analysis ◽  
Theoretical Formulation ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element ◽  
Element Method

Abstract A hybrid finite element method for computing mid-frequency vibrations is presented. In the mid-frequency region a system is comprised by some members that contain several wavelengths and some members that contain a small number of wavelengths within their dimensions. The former are considered long members and they are modeled by the Energy Finite Element Analysis (EFEA). The latter are considered short and they are modeled by the Finite Element Analysis (FEA). In this paper the excitation is considered to be applied on the short members. The hybrid formulation computes the response of the entire system. The characteristics of the long members affect the behavior of the short members and the amount of power flow between the members of the system. The resonant characteristics of the short members and the boundary conditions imposed by the long members determine the amount of input power into the system. The interaction between members is described by a set of equations between the FEA and the EFEA primary variables at the interfaces between long and short members. The equations for the short and the long members and the interface equations are solved simultaneously. A theoretical formulation and a numerical implementation for systems that contain one wave type is presented. Analytical solutions for several co-linear beam configurations are compared to numerical results produced by the hybrid finite element method. Good correlation is observed for all analyses.

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