scholarly journals Closed-Form Solution for Secondary Perturbation Displacement in Finite-Element-Implemented Koiter’s Theory

AIAA Journal ◽  
2020 ◽  
Vol 58 (4) ◽  
pp. 1785-1795
Author(s):  
Jiayi Yan ◽  
Shuguang Li
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution

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.

Generalized and Simplified Linear Closed-Form Solution of an Active Tensegrity Unit in the Form of Octahedral Cell

2014 ◽  
Vol 969 ◽  
pp. 192-198
Author(s):  
Stanislav Kmeť ◽  
Peter Platko
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Closed Form ◽  
Closed Form Solution ◽  
Point Load ◽  
Form Solution ◽  
Cable System ◽  
Form Analysis ◽  
Tensile Forces

Results of the generalized and simplified linear closed form solution of an active or adaptive tensegrity unit, as well as its numerical analysis using finite element method are presented in the paper. The shape of the unit is an octahedral cell with a square base and it is formed by thirteen members (four bottom and four top cables, four edge struts and one central strut). The central strut is designed as an actuator that allows for an adjustment of the shape of the unit which leads to changes of tensile forces in the cables. Due to the diagonal symmetry of the 3D tensegrity unit the closed-form analysis is based on the 2D solution of the equivalent planar biconvex cable system with one central strut under a vertical point load.

Study of Combined Heat and Mass Transfer From Fins Using Non-Dimensional Finite Element Formulation

2013 ◽  
Author(s):  
Sulaman Pashah ◽  
Syed M. Zubair ◽  
Abul Fazal M. Arif
Keyword(s):  
Mass Transfer ◽  
Finite Element ◽  
Closed Form ◽  
Heat And Mass Transfer ◽  
Closed Form Solution ◽  
Base Material ◽  
Form Solution ◽  
Element Formulation ◽  
Dimensionless Parameters ◽  
Dimensional Finite Element

The use of dimensional analysis and dimensionless parameters is very common in the field of heat transfer. The paper presents a non-dimensional finite element capable of modeling combined heat and mass transfer from fins. The aim of the formulation is to get solution of the fin problems that do not have a closed form solution. The performance of a fin is described through its efficiency and numerous closed form solutions for fin efficiency under combined heat and mass transfer are available in the literature. Deriving a closed form solution for geometric or material complexities is somewhat a difficult task. An example is variable profile composite fin. A composite fin is composed of base material or substrate with a coating layer. Finite element approach can handle such complexity with relatively ease, Therefore the main objective is to developed formulation for mass transfer problems. The formulation is derived in dimensionless form to extend the applicability of finite element results to a class of problems with same governing dimensionless parameters. The derived formulation is then applied to study the combined heat and mass transfer for variable profile composite fins under fully wet condition.

On the Numerical Implementation of Elastoplastic Models

1984 ◽  
Vol 51 (2) ◽  
pp. 283-288 ◽  
Author(s):  
P. J. Yoder ◽  
R. G. Whirley
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Computational Efficiency ◽  
Kinematic Hardening ◽  
Closed Form Solution ◽  
Form Solution ◽  
Perturbation Solution ◽  
Numerical Implementation ◽  
Time Step ◽  
Trade Offs

A closed-form solution is given for the way stresses evolve during an elastoplastic time step under conditions of purely kinematic hardening or softening. When isotropic effects are included, the analysis becomes more difficult, so a perturbation solution is developed. These solutions are then compared with various algorithms commonly used in finite element programs in order to assess the trade-offs between accuracy and computational efficiency.

Material Property Identification of Artificial Degenerated Intervertebral Disc Models — Comparison of Inverse Poroelastic Finite Element Analysis with Biphasic Closed Form Solution

2013 ◽  
Vol 29 (4) ◽  
pp. 589-597 ◽  
Author(s):  
M. Nikkhoo ◽  
Y.-C. Hsu ◽  
M. Haghpanahi ◽  
M. Parnianpour ◽  
J.-L. Wang
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Intervertebral Disc ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Hydraulic Permeability ◽  
Element Analysis ◽  
Property Identification

ABSTRACTDisc rheological parameters regulate the mechanical and biological function of intervertebral disc. The knowledge of effects of degeneration on disc rheology can be beneficial for the design of new disc implants or therapy. We developed two material property identification protocols, i.e., inverse poroelas-tic finite element analysis, and biphasic closed form solution. These protocols were used to find the material properties of intact, moderate and severe degenerated porcine discs. Comparing these two computational protocols for intact and artificial degenerated discs showed they are valid in defining bi-phasic/poroelastic properties. We found that enzymatic agent disrupts the functional interactions of proteoglycans which decreased hydraulic permeability and aggregate modulus but increased the Poisson's ratio. The fatigue loading, which damages disc structure, and squeezes and occludes the matrix pores, further decreased the hydraulic permeability and the Poisson's ratio but increased the elastic modulus. The FE simulations showed the stress experienced during the creep test increases with severe degeneration but steady-state fluid loss decreases for the both moderate and severe degenerated discs. Discriminant analysis declared that the probability of correct classification using the FE analysis is higher than the results of the closed form solution. The specimen-specific models extracted from FE analysis can be additionally used for complimentary investigations on disc biomechanics.

NEUROFUZZY MODELING OF NATURAL FREQUENCIES OF CYLINDRICAL SHELLS APPLIED TO EVOLUTIONARY BASED OPTIMAL DESIGN OF SR MOTORS

2006 ◽  
Vol 03 (03) ◽  
pp. 263-277 ◽  
Author(s):  
HOSSEIN ROUHANI ◽  
MANSOUR NIKKHAH BAHRAMI ◽  
BABAK NADJAR ARAABI ◽  
CARO LUCAS
Keyword(s):  
Finite Element ◽  
Optimal Design ◽  
Closed Form ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Closed Form Solution ◽  
Form Solution ◽  
Design Problems ◽  
Special Cases ◽  
Wide Range

A thorough analysis of cylindrical shells' dynamical behavior is essential in many different industrial design problems, and particularly in electric motor design. Shell vibration equations form a set of partial differential equations of order eight, where their closed form solution is only known for few special cases with a few known boundary conditions along with many not necessarily realistic assumptions. On the other hand, finite element based numerical solutions does not yield a lumped model that can be regarded as a general solution for natural frequencies of cylindrical shells. In this paper, a neurofuzzy model for natural frequencies of cylindrical shells is developed. At first, natural frequencies are calculated for a wide range of cylindrical shells' dimensions, using either closed form solution or finite element method. Gathered data is exploited for training of a Locally Linear Neurofuzzy Network, which yields a general model for calculation of natural frequencies of cylindrical shells. While the developed neurofuzzy model may be used in different design problems that deals with cylindrical shells, as a case study, the proposed model along with an evolutionary algorithm are utilized in the optimal design of a Switched Reluctance motor.

Semi-Closed-Form Displacement Equations for Calculating J-R Curves From Pipe Fracture Experiments

2015 ◽  
Author(s):  
Richard Olson ◽  
Ben Thornton
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Strain Curve ◽  
Compact Tension ◽  
Compact Tension Specimen ◽  
Form Solution ◽  
Finite Element Analyses ◽  
Pipe Bend ◽  
Point Bend

The equations to generate a J-R curve from a four-point bend test on circumferentially cracked pipe have been known for many years. Given the experimental pipe load-displacement record and crack growth, the only impediment to routinely calculating pipe J-R curves is the requirement to know the non-cracked pipe elastic and plastic displacements. Traditionally, finite element analyses are used to find these displacements. This paper presents a semi-closed-form solution for the total (elastic plus plastic) non-cracked pipe displacements that eliminates the need to perform finite element analyses to calculate a pipe J-R curve. Using a Ramberg-Osgood nonlinear representation of the stress-strain curve and the assumption that plane sections remain plane, beam bending equations can be written to find nonlinear beam displacements for pipe bend geometries with a base metal crack. Building on this result, the solution is extended to the dissimilar metal weld (DMW) case with five nonlinear materials. The non-cracked pipe displacement solutions are presented as well as comparisons using these equations between compact tension specimen J-R toughness curves and J-R curves from pipe experiments.

Non-Dimensional Finite Element Formulation for Thermal Problems

2012 ◽  
Author(s):  
Sulaman Pashah ◽  
Abul Fazal M. Arif ◽  
Syed M. Zubair
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Finite Element Approach ◽  
Fin Efficiency ◽  
Dimensional Finite Element ◽  
Element Approach

The use of dimensional analysis and dimensionless parameters is very common in the field of heat transfer; nevertheless the concept of non-dimensional finite element formulation has been applied to a limited type of thermo-fluid problems. The non-dimensional finite element method should provide the dimensionless solution for a given problem. The aim of present work is to develop a non-dimensional thermal finite element for getting dimensionless solution of the problems that do not have a closed form solution. An example is a fin (or extended surface) design. Fin efficiency is a performance characteristic that can be used as design criterion; thus closed form dimensionless solutions for fin efficiency are available in the literature. The results are for different geometry, single material fins. In case, if the fin problem has some geometric and/or material complexities then closed form solutions are not available and finite element approach can be used. However, the obtained finite element solution would not be in dimensionless form. For example, no closed form solutions are available for variable thickness composite fins (i.e. a fin having a base material with a coating over its surface), and the literature shows that finite element solution has been used to study thermal performance of the variable thickness composite fins. Therefore, non-dimensional finite element approach can be applied to directly obtain the dimensionless solution for the problem. The current work consists of presenting a non-dimensional finite element formulation for thermal problems. The element formulation is first validated by solving a test case study that has known closed form solution. The objective is to demonstrate the usefulness of the non-dimensional finite element approach by obtaining dimensionless finite element solutions for some applied problems that do not have a closed form solution.

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