Finite Element Analysis: Mathematical Theory and Applications
نویسندگان
چکیده
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v 1 Mathematical Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Function Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Variational Form of Differential Equations . . . . . . . . . . . . . . 4 1.3 Key Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 Finite Element Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1 Definition and Construction of Finite Elements . . . . . . . . . . . 11 2.2 Key Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3 Error of the Finite Element Method . . . . . . . . . . . . . . . . . . . . . 15 3.1 Key Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4 Worked Examples and Applications . . . . . . . . . . . . . . . . . . . . . 19 4.1 Worked Examples with MATLAB Approximation . . . . . . . . . . 19 4.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Vita . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
منابع مشابه
Free Vibration Analysis of Nanoplates Made of Functionally Graded Materials Based On Nonlocal Elasticity Theory Using Finite Element Method
In this paper, an analysis of free vibration in functionally graded nanoplate is presented. Third-order shear deformation plate theory is used to reach more accuracy in results. Small-scale effects are investigated using Eringen`s nonlocal theory. The governing equations of motion are obtained by Hamilton`s principle. It is assumed that the properties of nanoplates vary through their thicknesse...
متن کاملA two dimensional Simulation of crack propagation using Adaptive Finite Element Analysis
Finite element method (FEM) is one of the most famous methods which has many applications in varies studies such as the study of crack propagation in engineering structures. However, unless extremely fine meshes are employed, problem arises in accurately modelling the singular stress field in the singular element area around the crack tip. In the present study, the crack growth simulation has b...
متن کاملNonlinear Finite Element Analysis of Bending of Straight Beams Using hp-Spectral Approximations
Displacement finite element models of various beam theories have been developed using traditional finite element interpolations (i.e., Hermite cubic or equi-spaced Lagrange functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation φ and/or shear strain γxz, or in the integral form u...
متن کاملA Comprehensive Mathematical Model for Analysis of WR-Resolvers under Stator Short Circuit Fault
Wound-Rotor (WR) resolvers are the most widely used position sensors in applications with harsh environmental conditions. However, their performance is exposed to failure due to the high risk of short circuit (SC) fault. Although the output current of the resolver is negligible, its thin copper wires increase the probability of the short circuit fault. To avoid the propagation of the turn-to-tu...
متن کاملExperimental and 3D Finite Element Analysis of a Slotless Air-Cored Axial Flux PMSG for Wind Turbine Application
In this research paper, the performance of an air-cored axial flux permanent magnet synchronous generator is evaluated for low speed, direct drive applications using 3D finite element modeling and experimental tests. The structure of the considered machine consists of double rotor and coreless stator, which results in the absence of core losses, reduction of stator weight and elimination of cog...
متن کاملFree Vibration Analysis of a Sloping-frame: Closed-form Solution versus Finite Element Solution and Modification of the Characteristic Matrices (TECHNICAL NOTE)
This article deals with the free vibration analysis and determination of the seismic parameters of a sloping-frame which consists of three members; a horizontal, a vertical, and an inclined member. The both ends of the frame are clamped, and the members are rigidly connected at joint points. The individual members of the frame are assumed to be governed by the transverse vibration theory of an ...
متن کامل