Large Displacement Analysis of Viscoelastic Beams and Frames by the Finite-Element Method

1974 ◽  
Vol 41 (3) ◽  
pp. 635-640 ◽  
Author(s):  
T. Y. Yang ◽  
G. Lianis
Keyword(s):  
Finite Element ◽  
Geometrical Nonlinearity ◽  
Approximate Solutions ◽  
Solution Procedure ◽  
Large Displacement ◽  
Cantilever Beams ◽  
The Finite Element Method ◽  
Stress Strain Relation ◽  
Linear Viscoelastic ◽  
Hereditary Integral

A finite-element displacement formulation and solution procedure are developed for the analysis of large displacement problems of viscoelastic beams and frames. The displacements considered are of the same order as the length of the beam member. The geometrical nonlinearity is accounted for by a midpoint-tangent incremental approach together with coordinate transformation at every step. The linear viscoelastic stress-strain relation in the form of hereditary integral is accounted for by the numerical integration with trapezoidal rule. Results are given for the displacements of a variety of beam and frame problems. For the simple case of cantilever beams, some alternative approximate solutions are available for comparison and reasonable agreement is indicated.

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.

scholarly journals A review of finite-element modelling in snow mechanics

2013 ◽  
Vol 59 (218) ◽  
pp. 1189-1201 ◽  
Author(s):  
E.A. Podolskiy ◽  
G. Chambon ◽  
M. Naaim ◽  
J. Gaume
Keyword(s):  
Finite Element ◽  
Approximate Solutions ◽  
Mechanics Of Solids ◽  
Model Parameters ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Essential Information ◽  
Snow Microstructure ◽  
Snow Mechanics

The finite-element method (FEM) is one of the main numerical analysis methods in continuum mechanics and mechanics of solids (Huebner and others, 2001). Through mesh discretization of a given continuous domain into a finite number of sub-domains, or elements, the method finds approximate solutions to sets of simultaneous partial differential equations, which express the behavior of the elements and the entire system. For decades this methodology has played an accelerated role in mechanical engineering, structural analysis and, in particular, snow mechanics. To the best of our knowledge, the application of finite-element analysis in snow mechanics has never been summarized. Therefore, in this correspondence we provide a table with a detailed review of the main FEM studies on snow mechanics performed from 1971 to 2012 (40 papers), for facilitating comparison between different mechanical approaches, outlining numerical recipes and for future reference. We believe that this kind of compact review in a tabulated form will produce a snapshot of the state of the art, and thus become an appropriate, timely and beneficial reference for any relevant follow-up research, including, for example, not only snow avalanche questions, but also modeling of snow microstructure and tire–snow interaction. To that end, this correspondence is organized according to the following structure. Table 1 includes all essential information about previously published FEM studies originally developed to investigate stresses in snow with all corresponding mechanical and numerical parameters. Columns in Table 1 provide references to particular studies, placed in chronological order. Rows correspond to the main model parameters and other details of each considered case.

Numerical Modeling of Optical Fibers Using the Finite Element Method and an Exact Non-reflecting Boundary Condition

2018 ◽  
Vol 18 (4) ◽  
pp. 581-601
Author(s):  
Rafail Z. Dautov ◽  
Evgenii M. Karchevskii
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Numerical Modeling ◽  
Optical Fibers ◽  
Original Problem ◽  
Approximate Solutions ◽  
The Finite Element Method ◽  
New Formulation ◽  
Adjoint Operators

AbstractThe original problem for eigenwaves of weakly guiding optical fibers formulated on the plane is reduced to a convenient for numerical solution linear parametric eigenvalue problem posed in a disk. The study of the solvability of this problem is based on the spectral theory of compact self-adjoint operators. Properties of dispersion curves are investigated for the new formulation of the problem. An efficient numerical method based on FEM approximations is developed. Error estimates for approximate solutions are derived. The rate of convergence for the presented algorithm is investigated numerically.

Vibration analysis of bi-stable composite cross-ply laminates using refined shape functions

2016 ◽  
Vol 51 (8) ◽  
pp. 1135-1148 ◽  
Author(s):  
A Firouzian-Nejad ◽  
S Ziaei-Rad ◽  
M Moore
Keyword(s):  
Finite Element ◽  
Composite Plates ◽  
Approximate Solutions ◽  
Element Model ◽  
Dynamic Responses ◽  
The Finite Element Method ◽  
Shape Functions ◽  
Design Modification ◽  
Qualitative And Quantitative ◽  
Applied Forces

In this article, static and dynamic responses of cross-ply bi-stable composite plates were studied. To accurately predict the natural frequencies and snap-through load, a set of higher order shape functions were proposed. In static analysis, the stable configurations, the deflection of corners, and the midpoint of the plate were calculated. For dynamic analysis, Hamilton’s principle is used to provide approximate solutions to the vibration problem under study. The responses of the plate under ramp and harmonic applied forces were determined, the effect of shape functions on the prediction of the first natural frequency of the plate and the required force for snap-through were investigated. A finite element model is also developed to study the static and vibration characteristics of bi-stable composite plate. The qualitative and quantitative comparisons between the finite element method results and those obtained from the present analysis are generally good and satisfactory. The developed analytical model can also be used for parametric study and further design modification.

An Introduction to the Finite Element Method Using MATLAB

2005 ◽  
Vol 33 (3) ◽  
pp. 260-277 ◽  
Author(s):  
Donald W. Mueller
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Engineering Students ◽  
Solid Mechanics ◽  
Solution Procedure ◽  
The Finite Element Method ◽  
Stepped Shaft ◽  
Systematic Solution ◽  
Force Equilibrium ◽  
Element Method

This paper outlines an efficient approach to introducing the finite element method to undergraduate mechanical engineering students. This approach requires that the students have prior experience with MATLAB and a fundamental understanding of solid mechanics. Only two-dimensional beam element problems are considered, to simplify the development. The approach emphasizes an orderly solution procedure and involves important finite element concepts, such as the stiffness matrix, element and global coordinates, force equilibrium, and constraints. Two important and challenging engineering problems — a statically indeterminate beam structure and a stepped shaft — are analyzed with the systematic solution procedure and a MATLAB program. The ability of MATLAB to manipulate matrices and solve matrix equations makes the computer solution concise and easy to follow. The flexibility associated with the computer implementation allows example problems to be easily modified into design projects.

scholarly journals Finite element modelling of rectangular concrete-filled steel tube stub columns incorporating high strength and ultra-high strength materials under concentric axial compression

2021 ◽  
Vol 15 (4) ◽  
pp. 74-87
Author(s):  
Thai Son ◽  
Cuong Ngo-Huu ◽  
Dinh Van Thuat
Keyword(s):  
Finite Element ◽  
Axial Compression ◽  
Geometrical Nonlinearity ◽  
Initial Imperfection ◽  
High Strength ◽  
Element Model ◽  
Steel Tube ◽  
Stress Strain Relation ◽  
Proposed Model ◽  
Stub Columns

This study presents a unified approach to simulate the behavior of rectangular concrete-filled steel stub columns incorporating high strength and ultra-high strength materials subjected to concentric axial compression. The finite element model is developed based on Abaqus software, which is capable of accounting for geometrical nonlinearity, material plasticity, and interaction between multi-physics. The proposed model incorporates the influences of residual stress for welded-box steel sections and initial imperfection. A novel stress-strain relation of confined concrete is proposed to account for the composite action, which might increase the strength and ductility of infilled concrete under multi-axial compressive conditions. Various verification examples are conducted with wide ranges of geometrical and material properties. The simulation results show that the proposed model can accurately predict the ultimate strength, load-deformation relations, and failure mode of the experimental specimens.

scholarly journals A NUMERICAL STUDY REGARDING THE INFLUENCE OF THE LONGITUDINAL EXTENT OF A T-SHAPED CRACK ON THE EIGENFREQUENCY DECREASE OF CANTILEVER BEAMS

2018 ◽  
Vol 24 (4) ◽  
pp. 50-55
Author(s):  
Cristian Tufisi ◽  
GILBERT-RAINER Gillich
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Relative Frequency ◽  
Numerical Study ◽  
Cantilever Beams ◽  
The Finite Element Method ◽  
Frequency Shifts ◽  
Shaped Crack ◽  
Bending Modes ◽  
Crack Position

The paper analyzes the effects of T-shaped cracks in beams regarding the manner in which the frequencies of the bending modes change. We determined the eigenfrequencies of the damaged beam involving the finite element method for five lengths of the branched crack’s longitudinal components and numerous crack locations. This permitted plotting the frequency shifts curves and calculating the relative frequency shifts. Afterward, we extracted the damage patterns for all crack types and one crack position. It was found that the patterns are quite similar, just differing by their amplitudes, thus by normalization the damage severity effect can be suppressed.

Beam and Truss Element for Non-Linear Geometric Analysis

2018 ◽  
Vol 35 ◽  
pp. 145-161
Author(s):  
Messaoud Bourezane
Keyword(s):  
Finite Element ◽  
Geometric Analysis ◽  
Large Displacement ◽  
The Finite Element Method ◽  
Exact Representation ◽  
Cross Sectional ◽  
Truss Element ◽  
Initial Area ◽  
Non Linear ◽  
Comparable Accuracy

The present paper investigates possible improvements to the performances of beam finite element with curvature correction where large slopes as well as large displacement are involved. The displacement field of the beam element is based on simple strain functions satisfying the requirement of exact representation of curvature. The truss element is introduced with the current cross sectional and the current length instead of initial area and initial length in large displacement solution. The finite element method is used in conjunction with linearised incrementation and the Newton-Raphson iterative technique. The two basic formulations to problem involving geometric non-linear, Eulerian and Lagrangian are also discussed. The present elements offer significant advantages over existing stiffness-based elements. Consequently, fewer elements are needed to yield results of comparable accuracy. This is demonstrated with the analysis of several simple example structures by comparing the results to those of stiffness based elements and analytical solution.

Analysis of Embedded and Surface Elliptical Flaws in Transversely Isotropic Bodies by the Finite Element Alternating Method

1991 ◽  
Vol 58 (2) ◽  
pp. 435-443 ◽  
Author(s):  
H. Rajiyah ◽  
S. N. Atluri
Keyword(s):  
Finite Element ◽  
Transversely Isotropic ◽  
Generalized Solution ◽  
Solution Procedure ◽  
Isotropic Case ◽  
The Finite Element Method ◽  
Crack Face ◽  
Elastic Symmetry ◽  
Alternating Method ◽  
Isotropic Bodies

The general analytical solution to the problem of a flat elliptical crack embedded in an infinite, transversely isotropic solid, oriented perpendicular to the axis of elastic symmetry, is derived along the lines of Vijayakumar and Atluri’s solution procedure for the isotropic case. The prior work of Kassir and Sih on this problem is limited to some constant and linear variations of normal and shear tractions on the crack face. The generalized solution is employed in the Schwarz-Neumann alternating method in conjunction with the finite element method. Such a method of analysis is shown to be an efficient way to evaluate the stress intensity factors along the flaw border.

scholarly journals A NUMERICAL STUDY REGARDING THE INFLUENCE OF THE LONGITUDINAL EXTENT OF A T-SHAPED CRACK ON THE EIGENFREQUENCY DECREASE OF CANTILEVER BEAMS

2019 ◽  
Vol 24 (4) ◽  
Author(s):  
CRISTIAN TUFISI ◽  
GILBERT-RAINER GILLICH
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Relative Frequency ◽  
Numerical Study ◽  
Cantilever Beams ◽  
The Finite Element Method ◽  
Frequency Shifts ◽  
Shaped Crack ◽  
Bending Modes ◽  
Crack Position

<p>The paper analyzes the effects of T-shaped cracks in beams regarding the manner in which the frequencies of the bending modes change. We determined the eigenfrequencies of the damaged beam involving the finite element method for five lengths of the branched crack’s longitudinal components and numerous crack locations. This permitted plotting the frequency shifts curves and calculating the relative frequency shifts. Afterward, we extracted the damage patterns for all crack types and one crack position. It was found that the patterns are quite similar, just differing by their amplitudes, thus by normalization the damage severity effect can be suppressed.</p>

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