On Solutions of Plane Strain Consolidation Problems by Finite Element Methods

1971 ◽  
Vol 8 (1) ◽  
pp. 109-118 ◽  
Author(s):  
C. T. Hwang ◽  
N. R. Morgenstern ◽  
D. W. Murray
Keyword(s):  
Finite Element ◽  
Numerical Analysis ◽  
Closed Form ◽  
Plane Strain ◽  
Excellent Agreement ◽  
Finite Element Methods ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Algebraic Equations ◽  
Closed Form Solutions

The formulation is presented of the equations governing the solution of true three-dimensional consolidation problems by means of finite element methods. The numerical procedure for handling the resulting algebraic equations is described briefly and detailed results from the solution of several problems are given. Excellent agreement is found between the numerical analysis and existing closed form solutions.

scholarly journals Finite Element Formulation of Fractional Constitutive Laws Using the Reformulated Infinite State Representation

2021 ◽  
Vol 5 (3) ◽  
pp. 132
Author(s):  
Matthias Hinze ◽  
André Schmidt ◽  
Remco I. Leine
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Constitutive Law ◽  
Benchmark Problems ◽  
Element Formulation ◽  
Algebraic Equations ◽  
State Representation ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Infinite State

In this paper, we introduce a formulation of fractional constitutive equations for finite element analysis using the reformulated infinite state representation of fractional derivatives. Thereby, the fractional constitutive law is approximated by a high-dimensional set of ordinary differential and algebraic equations describing the relation of internal and external system states. The method is deduced for a three-dimensional linear viscoelastic continuum, for which the hydrostatic and deviatoric stress-strain relations are represented by a fractional Zener model. One- and two-dimensional finite elements are considered as benchmark problems with known closed form solutions in order to evaluate the performance of the scheme.

Optimum Design for the Frame of Open Type Abrasive Flow Polish Machine

2012 ◽  
Vol 497 ◽  
pp. 89-93
Author(s):  
Liang Liang Yuan ◽  
Ke Hua Zhang ◽  
Li Min
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Finite Element Methods ◽  
Optimization Design ◽  
Low Cost ◽  
Three Dimensional ◽  
Force Model ◽  
Optimization Analysis ◽  
Open Type ◽  
Set Up

In order to process heterotype hole of workpiece precisely, an open abrasive flow polish machine is designed, and the optimization design of machine frame is done for low cost. Firstly, basing on the parameters designed with traditional ways, three-dimensional force model is set up with the soft of SolidWorks. Secondly, the statics and modal analysis for machine body have been done in Finite element methods (FEM), and then the optimization analysis of machine frame has been done. At last, the model of rebuild machine frame has been built. Result shows that the deformation angle value of machine frame increased from 0.72′ to 1.001′, the natural frequency of the machine decreased from 75.549 Hz to 62.262 Hz, the weight of machine decreased by 74.178 Kg after optimization. It meets the strength, stiffness and angel stiffness requirement of machine, reduces the weight and cost of machine.

Solutions to the Vector Tetrahedron Equation

1965 ◽  
Vol 87 (2) ◽  
pp. 228-234 ◽  
Author(s):  
Milton A. Chace
Keyword(s):  
Closed Form ◽  
Digital Computer ◽  
Three Dimensional ◽  
Dimensional Vector ◽  
Spherical Coordinates ◽  
Tetrahedron Equation ◽  
Position Determination ◽  
Closed Form Solutions

A set of nine closed-form solutions are presented to the single, three-dimensional vector tetrahedron equation, sum of vectors equals zero. The set represents all possible combinations of unknown spherical coordinates among the vectors, assuming the coordinates are functionally independent. Optimum use is made of symmetry. The solutions are interpretable and can be evaluated reliably by digital computer in milliseconds. They have been successfully applied to position determination of many three-dimensional mechanisms.

Aerodynamic study of three-dimensional larynx models using finite element methods

2008 ◽  
Vol 311 (1-2) ◽  
pp. 39-55 ◽  
Author(s):  
Marcelo de Oliveira Rosa ◽  
José Carlos Pereira
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Three Dimensional

Consistent Hydrodynamic Mass for Parallel Prismatic Beams in a Fluid-Filled Container

1984 ◽  
Vol 106 (3) ◽  
pp. 270-275
Author(s):  
J. F. Loeber
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Incompressible Fluid ◽  
Finite Element Methods ◽  
Mass Matrix ◽  
Three Dimensional ◽  
Beam Length ◽  
Step Process ◽  
Beam Bending

In this paper, representation of the effects of incompressible fluid on the dynamic response of parallel beams in fluid-filled containers is developed using the concept of hydrodynamic mass. Using a two-step process, first the hydrodynamic mass matrix per unit (beam) length is derived using finite element methods with a thermal analogy. Second, this mass matrix is distributed in a consistent mass fashion along the beam lengths in a manner that accommodates three-dimensional beam bending plus torsion. The technique is illustrated by application to analysis of an experiment involving vibration of an array of four tubes in a fluid-filled cylinder.

Three-Dimensional Computations of Transport and Growth for Crystal Growth Systems

2000 ◽  
Author(s):  
Jeffrey J. Derby ◽  
Andrew Yeckel
Keyword(s):  
Finite Element ◽  
Crystal Growth ◽  
Finite Element Methods ◽  
Three Dimensional ◽  
Bulk Crystal ◽  
Time Dependent ◽  
Engineering Systems ◽  
Bulk Crystal Growth ◽  
Strongly Nonlinear ◽  
Parallel Supercomputers

Abstract Modern finite element methods implemented on parallel supercomputers promise to allow the study of three-dimensional, time-dependent continuum phenomena in many engineering systems. This paper shows several examples of the fruitful application of these approaches to bulk crystal growth systems, where strongly nonlinear coupled phenomena are important.

Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

2013 ◽  
Vol 856 ◽  
pp. 147-152
Author(s):  
S.H. Adarsh ◽  
U.S. Mallikarjun
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Element Analysis ◽  
Complex Behaviour ◽  
Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

Sign in / Sign up

Export Citation Format

Share Document