Deformation analysis of lumbar spine based on mechanics of materials and finite element method

2017 ◽  
Author(s):  
Haiyun Chen ◽  
Yu Sun ◽  
Qi Zhang ◽  
Ying Hu ◽  
Yongmei Sun
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Lumbar Spine ◽  
Deformation Analysis ◽  
Mechanics Of Materials ◽  
Element Method

The Finite-Element Method—Part I

1989 ◽  
Author(s):  
Shiro Kobayashi ◽  
Soo-Ik Oh ◽  
Taylan Altan
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Ritz Method ◽  
Approximate Solutions ◽  
Plane Elasticity ◽  
Heat Transfer Analysis ◽  
Deformation Analysis ◽  
The Finite Element Method ◽  
Element Method

The concept of the finite-element procedure may be dated back to 1943 when Courant approximated the warping function linearly in each of an assemblage of triangular elements to the St. Venant torsion problem and proceeded to formulate the problem using the principle of minimum potential energy. Similar ideas were used later by several investigators to obtain the approximate solutions to certain boundary-value problems. It was Clough who first introduced the term “finite elements” in the study of plane elasticity problems. The equivalence of this method with the well-known Ritz method was established at a later date, which made it possible to extend the applications to a broad spectrum of problems for which a variational formulation is possible. Since then numerous studies have been reported on the theory and applications of the finite-element method. In this and next chapters the finite-element formulations necessary for the deformation analysis of metal-forming processes are presented. For hot forming processes, heat transfer analysis should also be carried out as well as deformation analysis. Discretization for temperature calculations and coupling of heat transfer and deformation are discussed in Chap. 12. More detailed descriptions of the method in general and the solution techniques can be found in References [3-5], in addition to the books on the finite-element method listed in Chap. 1. The path to the solution of a problem formulated in finite-element form is described in Chap. 1 (Section 1.2). Discretization of a problem consists of the following steps: (1) describing the element, (2) setting up the element equation, and (3) assembling the element equations. Numerical analysis techniques are then applied for obtaining the solution of the global equations. The basis of the element equations and the assembling into global equations is derived in Chap. 5. The solution satisfying eq. (5.20) is obtained from the admissible velocity fields that are constructed by introducing the shape function in such a way that a continuous velocity field over each element can be denned uniquely in terms of velocities of associated nodal points.

THE NUMERICAL MANIFOLD METHOD: A REVIEW

2010 ◽  
Vol 07 (01) ◽  
pp. 1-32 ◽  
Author(s):  
GUOWEI MA ◽  
XINMEI AN ◽  
LEI HE
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Distinct Element ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Integration Scheme ◽  
Numerical Manifold Method ◽  
Strong Discontinuities ◽  
Numerical Manifold ◽  
Element Method

This paper presents a review on the numerical manifold method (NMM), which covers the basic theories of the NMM, such as NMM components, NMM displacement approximation, formulations of the discrete system of equations, integration scheme, imposition of the boundary conditions, treatment of contact problems involved in the NMM, and also the recent developments and applications of the NMM. Modeling the strong discontinuities within the framework of the NMM is specially emphasized. Several examples demonstrating the capability of the NMM in modeling discrete block system, strong discontinuities, as well as weak discontinuities are given. The similarities and distinctions of the NMM with various other numerical methods such as the finite element method (FEM), the extended finite element method (XFEM), the generalized finite element method (GFEM), the discontinuous deformation analysis (DDA), and the distinct element method (DEM) are investigated. Further developments on the NMM are suggested.

An Application of Finite-Element Method To The Deformation Analysis of Coated Plain-Weave Fabrics

1982 ◽  
Vol 11 (4) ◽  
pp. 310-327
Author(s):  
H. Irokazu ◽  
M. Inami ◽  
Yoshio Nakahara
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Uniaxial Stress ◽  
Deformation Analysis ◽  
Strength Analysis ◽  
The Finite Element Method ◽  
Membrane Structures ◽  
Plain Weave ◽  
Weave Fabric ◽  
Element Method

Methods for analysing coated plain-weave fabric which has properties of nonlinear elasticity have not yet been satisfactorily developed. In this paper, a method which is promis ing for use in engineering applications like the strength analysis of membrane structures is presented. The finite element method using a rectangular element consisting of plain-weave fabric and coating material which is assumed to be an isotropic elastic plate of plane stress is applied to the method. Verification of the me thod is made by using uniaxial stress-strain responses. A square piece of coated plain-weave fabric with a square hole in it is analyzed as an example of application of the present method. Key Words: coated plain-weave fabrics; finite element method; nonlinearly elastic biaxial response; geometrically nonlinear prob lem ; incremental approach.

Geometric and Material Property Study of the Human Lumbar Spine Using the Finite Element Method

1992 ◽  
Vol 5 (4) ◽  
pp. 50-59 ◽  
Author(s):  
W. Suwito ◽  
T. S. Keller ◽  
P. K. Basu ◽  
A. M. Weisberger ◽  
A. M. Strauss ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Lumbar Spine ◽  
Material Property ◽  
The Finite Element Method ◽  
Human Lumbar Spine ◽  
Element Method
Sign in / Sign up

Export Citation Format

Share Document