A new three-dimensional shell theory in general (non-lines-of-curvature) coordinates for analysis of curved panels weakened by through/part-through holes

2009 ◽  
Vol 89 (2) ◽  
pp. 321-332 ◽  
Author(s):  
Reaz A. Chaudhuri
Keyword(s):  
Shell Theory ◽  
Three Dimensional ◽  
Lines Of Curvature ◽  
Curvature Coordinates ◽  
Curved Panels

Notes on Nonlinear Shell Theory

1968 ◽  
Vol 35 (2) ◽  
pp. 393-401 ◽  
Author(s):  
Bernard Budiansky
Keyword(s):  
Shell Theory ◽  
Small Perturbations ◽  
Membrane Shell ◽  
Nonlinear Shell Theory ◽  
Lines Of Curvature ◽  
Curvature Coordinates ◽  
Nonlinear Shell ◽  
Membrane Shells ◽  
Initial Strains ◽  
Approximate Equations

Exact tensor equations of equilibrium are derived for nonlinear membrane shell theory and small perturbations of pressurized membrane shells. Approximate equations (for sufficiently small initial strains and rotations) for small perturbations of pressurized membrane shells are also given. Exact equations for the general nonlinear shell theory (including bending) are discussed, and approximate equations (again for small initial strains and rotations) are derived for the small perturbations, buckling, and vibration of stressed shells. These last equations are given in an Appendix in lines-of-curvature coordinates in classical notation.

scholarly journals Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Energy Density ◽  
Constitutive Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

Three-Dimensional Vibration Analysis of Thick, Complete Conical Shells

2004 ◽  
Vol 71 (4) ◽  
pp. 502-507 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa
Keyword(s):  
Present Method ◽  
Shell Theory ◽  
Ritz Method ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Algebraic Polynomials ◽  
Shells Of Revolution ◽  
Conical Shells ◽  
Thin Shell Theory ◽  
Time Periodic

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution. Unlike conventional shell theories, which are mathematically two-dimensional (2D), the present method is based upon the 3D dynamic equations of elasticity. Displacement components ur,uz, and uθ in the radial, axial, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the r and z-directions. Potential (strain) and kinetic energies of the conical shells are formulated, the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the conical shells. Novel numerical results are presented for thick, complete conical shells of revolution based upon the 3D theory. Comparisons are also made between the frequencies from the present 3D Ritz method and a 2D thin shell theory.

Effect of truck position and multiple truck loading on response of long-span metal culverts

2014 ◽  
Vol 51 (2) ◽  
pp. 196-207 ◽  
Author(s):  
Tamer M. Elshimi ◽  
Richard W.I. Brachman ◽  
Ian D. Moore
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Shell Theory ◽  
Orthotropic Shell ◽  
Three Dimensional ◽  
Element Analysis ◽  
Long Span ◽  
Dimensional Finite Element ◽  
Current Design ◽  
Three Dimensional Finite Element

Long-span metal culverts have been used for almost 50 years as an economical alternative to short-span bridges. Current design methods are based on two-dimensional finite element analysis using beam theory to represent the structure, or three-dimensional analysis employing orthotropic shell theory. However, neither analysis has been used to investigate the most critical position for trucks at the surface of long-span metal culverts. This paper shows results of three-dimensional finite element analysis, employing orthotropic shell theory and explicitly modeling the geometry of corrugated plates for a specific box culvert tested using a fully loaded dump truck. The analysis was then extended to study the effect of truck position on the response of long-span box and arch culverts. The finite element models, employing orthotropic shell theory and explicitly modeling the geometry of corrugated plates, successfully produced the behaviour of the culvert under truck loading for different truck positions. Culvert deformations were calculated within 7%–13% of the measured values at different locations. The bending moment at the crown was within 4%–17% of the values calculated using the measured strains. If three-dimensional finite element analysis is used to design these culverts, two design trucks should be considered (current design considers a single design truck). The highest moment or thrust is obtained when the truck tandem axles are located above the crown of the culvert.

Bifurcation of Equilibrium in Thick Orthotropic Cylindrical Shells Under Axial Compression

1995 ◽  
Vol 62 (1) ◽  
pp. 43-52 ◽  
Author(s):  
G. A. Kardomateas
Keyword(s):  
Axial Compression ◽  
Orthotropic Material ◽  
Shell Theory ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Elasticity Solution ◽  
Timoshenko Theory ◽  
Cylinder Axis ◽  
Dimensional Theory ◽  
Nonshallow Shell

The bifurcation of equilibrium of an orthotropic thick cylindrical shell under axial compression is studied by an appropriate formulation based on the three-dimensional theory of elasticity. The results from this elasticity solution are compared with the critical loads predicted by the orthotropic Donnell and Timoshenko nonshallow shell formulations. As an example, the cases of an orthotropic material with stiffness constants typical of glass/epoxy and the reinforcing direction along the periphery or along the cylinder axis are considered. The bifurcation points from the Timoshenko formulation are always found to be closer to the elasticity predictions than the ones from the Donnell formulation. For both the orthotropic material cases and the isotropic one, the Timoshenko bifurcation point is lower than the elasticity one, which means that the Timoshenko formulation is conservative. The opposite is true for the Donnell shell theory, i.e., it predicts a critical load higher than the elasticity solution and therefore it is nonconservative. The degree of conservatism of the Timoshenko theory generally increases for thicker shells. Likewise, the Donnell theory becomes in general more nonconservative with thicker construction.

scholarly journals The Analysis and Calculation of DC Earth Electrode Electric Field Coupling with Thermal based on Shell Theory

2017 ◽  
Author(s):  
Jingli Li ◽  
Liying Guo ◽  
Peng Hu ◽  
Yuanbo Li ◽  
Yu Zhang ◽  
...  
Keyword(s):  
Electric Field ◽  
Thermal Field ◽  
Shell Theory ◽  
Three Dimensional ◽  
Dynamic Coupling ◽  
Electrode Structure ◽  
Electrical Field ◽  
Field Coupling ◽  
Dc Current ◽  
Earth Electrode

During HVDC earth return operation systems, a high magnitude current will be injected into soil through earth electrode, the potential on the surface would change widely and produce unfavorable effects on the AC systems around. This paper presents an effective finite element method (FEM) coupling electric field with thermal field to evaluate the electrical field induced by the injected DC current. Firstly, owe to the characteristic of FEM, this method can consider arbitrary soil and earth electrode structure. Secondly, by setting the electrical and thermal parameters of soil as a function of temperature at the same time, the dynamic coupling process of electric field and thermal field is simulated accurately. Thirdly, to deal with the singular point in FEM subdivision and the huge computation in traditional three-dimensional FEM, the FEM coupling 2-D earth electrode with 3-D soil based on "shell" theory is introduced. Finally, based on the suggested method, the effect of abnormal resistance region (ARR) near DC earth electrode on electric field distribution is analyzed.

scholarly journals Isogeometric iFEM Analysis of Thin Shell Structures

Sensors ◽  
2020 ◽  
Vol 20 (9) ◽  
pp. 2685 ◽  
Author(s):  
Adnan Kefal ◽  
Erkan Oterkus
Keyword(s):  
Large Scale ◽  
Shell Theory ◽  
Weighted Least Squares ◽  
Three Dimensional ◽  
Shell Element ◽  
Surface Strain ◽  
Curvilinear Coordinates ◽  
Shell Structures ◽  
Engineering Structures ◽  
Shape Sensing

Shape sensing is one of most crucial components of typical structural health monitoring systems and has become a promising technology for future large-scale engineering structures to achieve significant improvement in their safety, reliability, and affordability. The inverse finite element method (iFEM) is an innovative shape-sensing technique that was introduced to perform three-dimensional displacement reconstruction of structures using in situ surface strain measurements. Moreover, isogeometric analysis (IGA) presents smooth function spaces such as non-uniform rational basis splines (NURBS), to numerically solve a number of engineering problems, and recently received a great deal of attention from both academy and industry. In this study, we propose a novel “isogeometric iFEM approach” for the shape sensing of thin and curved shell structures, through coupling the NURBS-based IGA together with the iFEM methodology. The main aim is to represent exact computational geometry, simplify mesh refinement, use smooth basis/shape functions, and allocate a lower number of strain sensors for shape sensing. For numerical implementation, a rotation-free isogeometric inverse-shell element (isogeometric Kirchhoff–Love inverse-shell element (iKLS)) is developed by utilizing the kinematics of the Kirchhoff–Love shell theory in convected curvilinear coordinates. Therefore, the isogeometric iFEM methodology presented herein minimizes a weighted-least-squares functional that uses membrane and bending section strains, consistent with the classical shell theory. Various validation and demonstration cases are presented, including Scordelis–Lo roof, pinched hemisphere, and partly clamped hyperbolic paraboloid. Finally, the effect of sensor locations, number of sensors, and the discretization of the geometry on solution accuracy is examined and the high accuracy and practical aspects of isogeometric iFEM analysis for linear/nonlinear shape sensing of curved shells are clearly demonstrated.

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.

Approximate Elasticity Solution for Orthotopic Cylinder Under Hydrostatic Pressure and Band Loads

1970 ◽  
Vol 37 (1) ◽  
pp. 101-108 ◽  
Author(s):  
A. P. Misovec ◽  
J. Kempner
Keyword(s):  
Approximate Solution ◽  
Shell Theory ◽  
Good Accuracy ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
External Pressure ◽  
Theory Of Elasticity ◽  
Numerical Comparison ◽  
Axial Loads ◽  
Special Case

An approximate solution to the Navier equations of the three-dimensional theory of elasticity for an axisymmetric orthotopic circular cylinder subjected to internal and external pressure, axial loads, and closely spaced periodic radial loads is developed. Numerical comparison with the exact solution for the special case of a transversely isotropic cylinder subjected to periodic band loads shows that very good accuracy is obtainable. When the results of the approximate solution are compared with previously obtained results of a Flu¨gge-type shell solution of a ring-reinforced orthotropic cylinder, it is found that the shell theory gives fairly accurate representations of the deformations and stresses except in the neighborhood of discontinuous loads. The addition of transverse shear deformations does not improve the accuracy of the shell solution.

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