A New Method for Analysing Large Elasto-Plastic Deformations of a Thin Cosserat Shell

2010 ◽  
Vol 224 (10) ◽  
pp. 2055-2071
Author(s):  
A Ghassemi ◽  
A Shahidi ◽  
M Farzin
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Weak Form ◽  
Isotropic Hardening ◽  
Cosserat Theory ◽  
Finite Element Scheme ◽  
Geometric Stiffness ◽  
Stiffness Matrices ◽  
Cosserat Surface ◽  
First Time

One of the best approaches for modelling the large deformation of shells is the Cosserat surface; however, the finite-element implementation of this model suffers from membrane and shear locking, especially for very thin shells. If the director vector is constrained to remain perpendicular to the mid-surface, during deformation, locking will be prevented. This constraint is in fact a limiting analysis of the Cosserat theory in which Kirchhoff's hypothesis is enforced. This has been considered for the first time. Simo's plastic approach is modified to implement the constrained director. This model includes both kinematic and isotropic hardening behaviours. A consistent elasto-plastic tangent modular matrix is extracted. Numerical solution is performed by interpolation of displacement on the whole domain, and a hierarchical finite-element scheme is developed. The principle of virtual work is used to obtain the weak form of the governing differential equations and the material and geometric stiffness matrices are derived through a linearization process. The validity and the accuracy of the method are illustrated by numerical examples.

scholarly journals Local Elastic and Geometric Stiffness Matrices for the Shell Element Applied in cFEM

2017 ◽  
Author(s):  
Dávid Visy ◽  
Sándor Ádány
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shell Element ◽  
Numerical Examples ◽  
Geometric Stiffness ◽  
Stiffness Matrices ◽  
Plane Element ◽  
Unusual Combination ◽  
Shell Finite Element ◽  
Lagrange Strain

In this paper local elastic and geometric stiffness matrices of ashell finite element are presented and discussed. The shell finiteelement is a rectangular plane element, specifically designedfor the so-called constrained finite element method. One of themost notable features of the proposed shell finite element isthat two perpendicular (in-plane) directions are distinguished,which is resulted in an unusual combination of otherwise classicshape functions. An important speciality of the derived stiffnessmatrices is that various options are considered, whichallows the user to decide how to consider the through-thicknessstress-strain distributions, as well as which second-order strainterms to consider from the Green-Lagrange strain matrix. Thederivations of the stiffness matrices are briefly summarizedthen numerical examples are provided. The numerical examplesillustrate the effect of the various options, as well as theyare used to prove the correctness of the proposed shell elementand of the completed derivations.

Application of Finite-Element Method to Interstiffener Buckling in Submersible Cylindrical Hulls

1983 ◽  
Vol 27 (04) ◽  
pp. 281-285
Author(s):  
K. Rajagopalan ◽  
C. Ganapathy Chettiar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computer Program ◽  
Cylindrical Shells ◽  
Geometric Stiffness ◽  
Stiffness Matrices ◽  
Finite Element Procedure ◽  
Stepwise Variation ◽  
Thin Walled

A finite-element procedure for the determination of buckling pressure of thin-walled cylindrical shells used in ocean structures is presented. The derivation of the elastic and geometric stiffness matrices is discussed in detail followed by a succinct description of the computer program developed by the authors during the course of this study for the determination of the buckling pressure. Particular attention is paid to the boundary conditions which strongly influence the buckling pressure. Applications involving the interstiffener buckling in submersible hulls and cylindrical shells with stepwise variation in wall thickness are considered and the results compared with the solutions and procedures available in the literature.

scholarly journals A Finite Element Formulation for Kirchhoff Plates in Strain-gradient Elasticity

2019 ◽  
Author(s):  
Alireza Beheshti
Keyword(s):  
Finite Element ◽  
Strain Gradient ◽  
Virtual Work ◽  
Hermite Polynomials ◽  
Gradient Elasticity ◽  
Weak Form ◽  
Element Formulation ◽  
Strain Gradient Elasticity ◽  
Rectangular Plates ◽  
Kirchhoff Plates

The current contribution is centered on bending of rectangular plates using the finite element method in the strain-gradient elasticity. To this aim, following introducing stresses and strains for a plate based on the Kirchhoff hypothesis, the principle of the virtual work is adopted to derive the weak form. Building upon Hermite polynomials and by deeming convergence requirements, four rectangular elements for the static analysis of strain-gradient plates are presented. To explore the performance of the proposed elements, particularly in small scales, some problems are solved and the results are compared with analytical solutions.

The Natural Frequency of the Shape Memory Alloy Anti-Symmetric Angle-Ply Composite Plates Using Finite Element Method

2014 ◽  
Vol 695 ◽  
pp. 52-55 ◽  
Author(s):  
Z.A. Rasid
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Geometric Stiffness ◽  
Stiffness Matrices ◽  
Element Method

Shape memory alloy (SMA) wires were embedded within laminated composite plates to take advantage of the shape memory effect (SME) property of the SMA. Active modal modification of SMAC plates was studied using the finite element method (FEM). A linear FEM formulation was developed based on the first order shear deformation theory. The effect of SMA was captured by adding the geometric stiffness matrix to the stiffness matrices of composite plates. Two methods of frequency improvements are considered here: The active property tuning (APT) and the active strain energy tuning (ASET) methods. The values of recovery stress for the ASET analysis were determined from Brinson’s model. The effects of several parameters on the natural frequencies of the SMAC plates were studied. It was found that the effect of SMA is similar for couples of frequency modes where frequencies of mode I and IV seems to have affected the most by SMA.

scholarly journals About an approximate method to solve the static boundary value problems in the isotropic hardening elastic-plastic solid

2006 ◽  
Vol 28 (2) ◽  
pp. 74-82
Author(s):  
Ngo Thanh Phong ◽  
Nguyen Thoi Trung ◽  
Nguyen Phu Vinh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Method ◽  
Weak Form ◽  
Theory Model ◽  
Isotropic Hardening ◽  
Mapping Algorithm ◽  
Elastic Plastic ◽  
Return Mapping ◽  
Return Mapping Algorithm

The paper presents the theory, model, weak form, finite element method and return-mapping algorithm for the isotropic hardening elastic-plastic problem. Then applying the algorithm to numerically simulate a variety of plane strain problems.

scholarly journals Finite Element Method modeling of Additive Manufactured Compressor Wheel

2021 ◽  
Author(s):  
Márton Tamás Birosz ◽  
Mátyás Andó ◽  
Sudhanraj Jeganmohan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Element Method Simulation ◽  
Element Model ◽  
Tensile Tests ◽  
Raw Material ◽  
Isotropic Hardening ◽  
Compressor Wheel ◽  
Material Extrusion ◽  
Element Method

AbstractDesigning components is a complex task, which depends on the component function, the raw material, and the production technology. In the case of rotating parts with higher RPM, the creep and orientation are essential material properties. The PLA components made with the material extrusion process are more resistant than VeroWhite (material jetting) and behave similarly to weakly cross-linked elastomers. Also, based on the tensile tests, Young’s modulus shows minimal anisotropy. Multilinear isotropic hardening and modified time hardening models are used to create the finite element model. Based on the measurements, the finite element method simulation was identified. The deformation in the compressor wheel during rotation became definable. It was concluded that the strain of the compressor wheel manufactured with material extrusion technology is not significant.

Finite element modeling of surge propagation and an application to the Hay River, N.W.T.

1992 ◽  
Vol 19 (3) ◽  
pp. 454-462 ◽  
Author(s):  
F. E. Hicks ◽  
P. M. Steffler ◽  
R. Gerard
Keyword(s):  
Finite Element ◽  
Channel Flow ◽  
Open Channel ◽  
Initial Conditions ◽  
Open Channel Flow ◽  
Kinematic Wave ◽  
Finite Element Scheme ◽  
Flow Problems ◽  
Ice Jam

This paper describes the application of the characteristic-dissipative-Galerkin method to steady and unsteady open channel flow problems. The robust performance of this new finite element scheme is demonstrated in modeling the propagation of ice jam release surges over a 500 km reach of the Hay River in Alberta and Northwest Territories. This demonstration includes the automatic determination of steady flow profiles through supercritical–subcritical transitions, establishing the initial conditions for the unsteady flow analyses. The ice jam releases create a dambreak type of problem which begins as a very dynamic situation then develops into an essentially kinematic wave problem as the disturbance propagated downstream. The characteristic-dissipative-Galerkin scheme provided stable solutions not only for the extremes of dynamic and kinematic wave conditions, but also through the transition between the two. Key words: open channel flow, finite element method, dam break, surge propagation.

An adaptive finite element scheme to solve fluid-structure vibration problems on non-matching grids

2001 ◽  
Vol 4 (2) ◽  
pp. 67-78 ◽  
Author(s):  
Ana Alonso ◽  
Anahí Dello Russo ◽  
César Otero-Souto ◽  
Claudio Padra ◽  
Rodolfo Rodríguez
Keyword(s):  
Finite Element ◽  
Adaptive Finite Element ◽  
Finite Element Scheme ◽  
Fluid Structure ◽  
Element Scheme ◽  
Structure Vibration ◽  
Vibration Problems

FINITE ELEMENT ANALYSIS OF PIEZOELECTRIC ELASTICITY WITH SINGULAR INPLANE ELECTROELASTIC FIELDS

2006 ◽  
Vol 03 (01) ◽  
pp. 115-135 ◽  
Author(s):  
MENG-CHENG CHEN ◽  
JIAN-JUN ZHU ◽  
K. Y. SZE
Keyword(s):  
Finite Element ◽  
Ad Hoc ◽  
Wedge Angle ◽  
Electric Displacement ◽  
Weak Form ◽  
Efficient Solutions ◽  
Element Formulation ◽  
Displacement Fields ◽  
Element Analysis ◽  
Electroelastic Fields

An ad hoc one-dimensional finite element formulation is developed for the eigenanalysis of inplane singular electroelastic fields at material and geometric discontinuities in piezoelectric elastic materials by using the eigenfunction expansion procedure and the weak form of the governing equations for prismatic sectorial domains composed of piezoelectrics, composites or air. The order of the electroelastic singularities and the angular variation of the stress and electric displacement fields are obtained with the formulation. The influence of wedge angle, polarization orientation, material types, and boundary and interface conditions on the singular electroelastic fields and the order of their singularity are also examined. The simplicity and accuracy of the formulation are demonstrated by comparison to several analytical solutions for piezoelectric and composite multi-material wedges. The nature and speed of convergence suggests that the present eigensolution could be used in developing hybrid elements for use along with standard elements to yield accurate and computationally efficient solutions to problems having complex global geometries leading to singular electroelastic states.

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