scholarly journals An advanced shell model for the analysis of geometrical and material nonlinear shells

2020 ◽  
Vol 66 (6) ◽  
pp. 1353-1376
Author(s):  
F. Gruttmann ◽  
W. Wagner
Keyword(s):  
Shell Model ◽  
Geometrical Nonlinearity ◽  
Local Equilibrium ◽  
Deformation Gradient ◽  
Computing Time ◽  
Strain Tensor ◽  
Shell Element ◽  
Field Equations ◽  
Residual Vector ◽  
Layered Shells

AbstractIn this paper layered shells subjected to static loading are considered. The displacements of the Reissner–Mindlin theory are enriched by a an additional part. These so-called fluctuation displacements include warping displacements and thickness changes. They lead to additional terms for the material deformation gradient and the Green–Lagrangian strain tensor. Within a nonlinear multi-field variational formulation the weak form of the boundary value problem accounts for the equilibrium of stress resultants and couple resultants, the local equilibrium of stresses, the geometrical field equations and the constitutive equations. For the independent shell strains an ansatz with quadratic shape functions is chosen. This leads to a significant improved convergence behaviour especially for distorted meshes. Elimination of a set of parameters on element level by static condensation yields an element stiffness matrix and residual vector of a quadrilateral shell element with the usual 5 or 6 nodal degrees of freedom. The developed model yields the complicated three-dimensional stress state in layered shells for elasticity and elasto-plasticity considering geometrical nonlinearity. In comparison with fully 3D solutions present 2D shell model requires only a fractional amount of computing time.

scholarly journals RESPON SEISMIK STRUKTUR RANGKA DINDING PENGISI YANG DIMODEL DENGAN ELEMEN SHELL PENUH DAN PARSIAL

2017 ◽  
Vol 5 (1) ◽  
Author(s):  
Putu Ratna Suryantini ◽  
M. Sukrawa ◽  
I. A. M Budiwati
Keyword(s):  
Shell Model ◽  
3D Structure ◽  
Shell Element ◽  
Maximum Load ◽  
3D Models ◽  
Frame Structure ◽  
Natural Period ◽  
Shell Elements ◽  
Frame Model ◽  
Wall Strength

Abstract: Research on the seismic response of in-filled frame structure has been done with in-filled frame model as full and partial shell elements. The wall is considered active until the maximum load on the full shell models, while the partial shell model using the gradual load with the strength of the wall is considered inactive if the stress of the wall exceeded the wall strength The 4 storey hotel building with full wall in x-direction and wall with opening in y-direction were modeled in SAP 2000 as 3D infilled-frame using full and partial shell element. In Mxy models, both wall were included in the model, while in My models, only the wall in y-direction included. Therefore, 4 models were obtained, there are full shell model MxyShPn and MyShPn and partial shell model MyShPar and MyShPar. In addition, 2 diagonal strut models MxyS and MyS  and an open frame model MOF were made as comparison. Prior to model 3D structure, validation models were created using test result condited by other as reference. For that purphose 5 2D models were created there are open frame model MOF, single strut model MST, multiple strut model MSG, full shell model MShPn and  partial shell model MShPar. From validation models, it is apparent that the MxyShPar model mimic the behavior of tested structure better than the other models. From the 3D models analysis result show that the displacement in x-direction of MxyShPn, MxyShPar, MxyS were 89%, 85%, 84% smaller than those of MOF, respectively inclusion of wall in the models, also reduce the internal forces and reduse the natural period of the sctructure.

A large deformation framework for shape memory polymers: Constitutive modeling and finite element implementation

2012 ◽  
Vol 24 (1) ◽  
pp. 21-32 ◽  
Author(s):  
Mostafa Baghani ◽  
Reza Naghdabadi ◽  
Jamal Arghavani
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Shape Memory ◽  
Finite Deformation ◽  
Deformation Gradient ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Shape Memory Polymers ◽  
Small Strain ◽  
Internal Variables

Shape memory polymers commonly experience both finite deformations and arbitrary thermomechanical loading conditions in engineering applications. This motivates the development of three-dimensional constitutive models within the finite deformation regime. In the present study, based on the principles of continuum thermodynamics with internal variables, a three-dimensional finite deformation phenomenological constitutive model is proposed taking its basis from the recent model in the small strain regime proposed by Baghani et al. (2012). In the constitutive model derivation, a multiplicative decomposition of the deformation gradient into elastic and inelastic stored parts (in each phase) is adopted. Moreover, employing the mixture rule, the Green–Lagrange strain tensor is related to the rubbery and glassy parts. In the constitutive model, the evolution laws for internal variables are derived during both cooling and heating thermomechanical loadings. Furthermore, we present the time-discrete form of the proposed constitutive model in the implicit form. Using the finite element method, we solve several boundary value problems, that is, tension and compression of bars and a three-dimensional beam made of shape memory polymers, and investigate the model capabilities as well as its numerical counterpart. The model is validated by comparing the predicted results with experimental data reported in the literature that shows a good agreement.

scholarly journals Collisional drift waves in stellarator plasmas

2003 ◽  
Vol 81 (12) ◽  
pp. 1309-1330
Author(s):  
J LV Lewandowski
Keyword(s):  
Magnetic Field ◽  
Equilibrium Model ◽  
Computational Study ◽  
Local Equilibrium ◽  
Edge Plasma ◽  
Drift Waves ◽  
Field Equations ◽  
Drift Wave ◽  
The Impact ◽  
The Magnetic Field

A computational study of resistive drift waves in the edge plasma of a stellarator with an helical magnetic axis is presented. Three coupled field equations, describing the collisional drift-wave dynamics in the linear approximation, are solved as an initial-value problem along the magnetic field line. The magnetohydrodynamic equilibrium is obtained from a three-dimensional local equilibrium model. The use of a local magnetohydrodynamic equilibrium model allows for a computationally efficient systematic study of the impact of the magnetic field structure on drift-wave stability. PACS Nos.: 52.35.Kt, 52.30.Jb, 52.35.Ra

scholarly journals Derivation of a refined six-parameter shell model: descent from the three-dimensional Cosserat elasticity using a method of classical shell theory

2020 ◽  
Vol 25 (6) ◽  
pp. 1318-1339 ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Shell Model ◽  
Shell Theory ◽  
Local Equilibrium ◽  
Three Dimensional ◽  
Simple Expression ◽  
Equilibrium Equations ◽  
Cosserat Elasticity ◽  
Shell Models ◽  
Classical Shell Theory ◽  
Derivation Method

Starting from the three-dimensional Cosserat elasticity, we derive a two-dimensional model for isotropic elastic shells. For the dimensional reduction, we employ a derivation method similar to that used in classical shell theory, as presented systematically by Steigmann (Koiter’s shell theory from the perspective of three-dimensional nonlinear elasticity. J Elast 2013; 111: 91–107). As a result, we obtain a geometrically nonlinear Cosserat shell model with a specific form of the strain energy density, which has a simple expression, with coefficients depending on the initial curvature tensor and on three-dimensional material constants. The explicit forms of the stress–strain relations and the local equilibrium equations are also recorded. Finally, we compare our results with other six-parameter shell models and discuss the relation to the classical Koiter shell model.

scholarly journals 2-D finite displacements and strain from particle imaging velocimetry (PIV) analysis of tectonic analogue models with TecPIV

Solid Earth ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 1123-1139 ◽  
Author(s):  
David Boutelier ◽  
Christoph Schrank ◽  
Klaus Regenauer-Lieb
Keyword(s):  
Software Package ◽  
Finite Strain ◽  
Deformation Gradient ◽  
Strain Tensor ◽  
Small Strain ◽  
Time Lapse ◽  
Image Correlation ◽  
Strain Rate Tensor ◽  
Analogue Models ◽  
Finite Displacements

Abstract. Image correlation techniques have provided new ways to analyse the distribution of deformation in analogue models of tectonics in space and time. Here, we demonstrate, using a new version of our software package (TecPIV), how the correlation of successive time-lapse images of a deforming model allows not only to evaluate the components of the strain-rate tensor at any time in the model but also to calculate the finite displacements and finite strain tensor. We illustrate with synthetic images how the algorithm produces maps of the velocity gradients, small-strain tensor components, incremental or instantaneous principal strains and maximum shear. The incremental displacements can then be summed up with Eulerian or Lagrangian summation, and the components of the 2-D finite strain tensor can be calculated together with the finite principal strain and maximum finite shear. We benchmark the measures of finite displacements using specific synthetic tests for each summation mode. The deformation gradient tensor is calculated from the deformed state and decomposed into the finite rigid-body rotation and left or right finite-stretch tensors, allowing the deformation ellipsoids to be drawn. The finite strain has long been the only quantified measure of strain in analogue models. The presented software package allows producing these finite strain measures while also accessing incremental measures of strain. The more complete characterisation of the deformation of tectonic analogue models will facilitate the comparison with numerical simulations and geological data and help produce conceptual mechanical models.

scholarly journals 2-D finite displacements and finite strain from PIV analysis of plane-strain tectonic analogue models

2019 ◽  
Author(s):  
David Boutelier ◽  
Christoph Schrank ◽  
Klaus Regenauer-Lieb
Keyword(s):  
Finite Strain ◽  
Deformation Gradient ◽  
Strain Tensor ◽  
Small Strain ◽  
Time Lapse ◽  
Complete Characterization ◽  
Image Correlation ◽  
Strain Rate Tensor ◽  
Analogue Models ◽  
Finite Displacements

Abstract. Image correlation techniques have provided new ways to analyze the distribution in space and time of deformation in analogue models of tectonics. Here we demonstrate how the correlation of successive time-lapse images of a deforming model allows not only to evaluate the components of the strain-rate tensor at any time in the model but also calculate the finite displacements and finite strain tensor. We illustrate, using synthetic images, the ability of the algorithm to produce maps of the velocity gradients, small-strain tensor components, but also incremental or instantaneous principal strains and maximum shear. The incremental displacements can then summed up using a Eulerian or a Lagrangian summation, and the components of the 2-D finite strain tensor can be calculated together with the finite principal strain and maximum finite shear. We benchmark the measures of finite displacements using specific synthetic tests for each summation mode. The deformation gradient tensor is calculated from the deformed state, and decomposed into the finite rigid-body rotation and left or right finite stretch tensors, allowing the deformation ellipsoids to be drawn. The finite strain has long been the only quantified measure of strain in analogue models. The presented software package allows producing these finite strain measures while also accessing incremental measures of strain. The more complete characterization of the deformation of tectonic analogue models will facilitate the comparison with numerical simulations and geological data, and help produce conceptual mechanical models.

Elastic-Plastic Modeling of Kinematic Hardening Materials Based on F=FeFp Decomposition and the Logarithmic Strain Tensor

Volume 1 ◽  
2004 ◽  
Author(s):  
Kamyar Ghavam ◽  
Reza Naghdabadi
Keyword(s):  
Kinematic Hardening ◽  
Deformation Gradient ◽  
Strain Tensor ◽  
Flow Rule ◽  
Deformation Gradient Tensor ◽  
Hardening Material ◽  
Elastic Plastic ◽  
Corotational Rate ◽  
Stress Components ◽  
Shear Problem

In this paper, based on the multiplicative decomposition of the deformation gradient tensor an elastic-plastic modeling of kinematic hardening materials is introduced. In this model, the elastic constitutive equation as well as the flow rule and hardening equation are expressed in terms of the corotational rate of the elastic and plastic logarithmic strains. As an application, the simple shear problem is solved and the stress components are plotted versus shear displacement for a kinematic hardening material.

NONLOCAL ANALYTICAL FLUGGE SHELL MODEL FOR AXIAL BUCKLING OF DOUBLE-WALLED CARBON NANOTUBES WITH DIFFERENT END CONDITIONS

NANO ◽  
2012 ◽  
Vol 07 (03) ◽  
pp. 1250018 ◽  
Author(s):  
HESSAM ROUHI ◽  
REZA ANSARI
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Shell Model ◽  
Ritz Method ◽  
Nonlocal Parameter ◽  
Geometrical Parameters ◽  
Field Equations ◽  
Axial Buckling ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

In this paper, a nonlocal Flugge shell model is utilized to investigate the axial buckling behavior of double-walled carbon nanotubes (DWCNTs) under various boundary conditions. According to the nonlocal elasticity theory, the displacement field equations coupled by the van der Waals interaction are derived. The set of governing equations of motion is then solved by the Rayleigh–Ritz method. The present analysis can treat boundary conditions in a layer-wise manner. The effects of nonlocal parameter, layer-wise boundary conditions and geometrical parameters on the mechanical behavior of DWCNTs are examined. Furthermore, molecular dynamics simulations are performed to assess the validity of the results and also to predict the appropriate values of nonlocal parameter. It is found that the type of boundary conditions affects the proper value of nonlocal parameter.

PROJECTED SHELL MODEL AND HIGH-SPIN SPECTROSCOPY

1995 ◽  
Vol 04 (04) ◽  
pp. 637-785 ◽  
Author(s):  
KENJI HARA ◽  
YANG SUN
Keyword(s):  
Shell Model ◽  
High Spin ◽  
Computing Time ◽  
Technical Information ◽  
Quantum Mechanical ◽  
Magic Numbers ◽  
Spin States ◽  
Axially Symmetric ◽  
Projected Shell Model ◽  
High Spin States

Most of the nuclei in the nuclear chart are deformed except for those in the vicinity of the magic numbers. It is difficult to treat such nuclei within the framework of the standard (spherical) shell model. On the other hand, the necessity for a proper quantum mechanical treatment of high-spin states has been steadily growing ever since modern experimental techniques made it possible to measure the fine details of the high-spin states of heavy nuclei. The present article reviews an approach based on the angular momentum projection technique which was initiated in the late seventies for the purpose of carrying out shell model configuration mixing calculations efficiently. A large number of examples is presented with an emphasis on the physical interpretation of the numerical results. Computing time for the whole spectrum up to spin ≈ 40 of an axially symmetric rare-earth nucleus takes only a few minutes on a Mainframe, showing the efficiency of the method. Most of the present calculations were carried out on a Workstation, but computation on a modern PC also presents no problem, so that one can enjoy a genuine quantum mechanical analysis of high-spin data using a facility available everywhere. Detailed technical information which may be useful for programming purposes is given in an Appendix.

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