Stress Analysis of Mitred Bends by Ring Elements

1984 ◽  
Vol 106 (1) ◽  
pp. 54-62 ◽  
Author(s):  
O. Watanabe ◽  
H. Ohtsubo
Keyword(s):  
Stress Analysis ◽  
Degrees Of Freedom ◽  
Shell Theory ◽  
Trigonometric Functions ◽  
Shape Functions ◽  
Straight Pipe ◽  
Shell Elements ◽  
Hermitian Polynomials ◽  
Ring Elements ◽  
Thin Shell Theory

This paper proposes a ring element for the stress analysis of mitred bends, which is an extension of ring elements for pipe bends proposed by the present authors. Since accurate treatments of continuity conditions on the connecting lines between straight pipe segments are employed and strain-displacement relations derived from the general thin shell theory with shear strains are considered, the present method can be applied to problems of mitred bends of complex configurations under general loading conditions. Shape functions are developed by trigonometric functions and Hermitian polynomials of second order in the circumferential and longitudinal directions, respectively. This finite element method requires fewer number of degrees of freedom for the same accuracy than the conventional shell elements.

Stress Analysis of Pipe Bends by Ring Elements

1978 ◽  
Vol 100 (1) ◽  
pp. 112-122 ◽  
Author(s):  
H. Ohtsubo ◽  
O. Watanabe
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Analysis ◽  
Finite Ring ◽  
Piping System ◽  
Pipe Length ◽  
Ring Method ◽  
Ring Elements ◽  
Thin Shell Theory ◽  
Element Method

This paper proposes a new finite element method for treating the stress analysis of a piping system under general loading conditions. This finite element method will be referred as the finite ring method, since its elements are ring-shaped. This finite ring treatment is based on the general thin shell theory incorporating shear and distributed deformations along the pipe length. In this paper, emphasis is given to the theoretical aspects of the method. A comparison with other experimental and theoretical results is presented to substantiate the validity of the present method.

Stress Analysis of Ellipsoidal Shell With Nozzle Under Internal Pressure Loading

1994 ◽  
Vol 116 (4) ◽  
pp. 431-436 ◽  
Author(s):  
V. N. Skopinsky ◽  
N. A. Berkov
Keyword(s):  
Internal Pressure ◽  
Stress Analysis ◽  
Shell Theory ◽  
Numerical Procedure ◽  
Graphical Form ◽  
Pressure Loading ◽  
Ellipsoidal Shell ◽  
Thin Shell Theory ◽  
Purpose Computer ◽  
Special Purpose Computer

This paper presents the numerical procedure for the stress analysis of the intersecting shells consisting of an ellipsoidal shell and nozzle. Thin shell theory and finite element method are used. The developed special-purpose computer program SAIS is employed for elastic stress analysis of the model joints of the ellipsoidal shell with nozzle. The parametric study of the joints under internal pressure loading was performed. The results are presented in graphical form. Nondimensional geometric parameters are considered to analyze the effects of changing these parameters on the maximum effective stresses in the shells.

scholarly journals Higher Order Multiscale Finite Element Method for Heat Transfer Modeling

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3827
Author(s):  
Marek Klimczak ◽  
Witold Cecot
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Higher Order ◽  
Shape Functions ◽  
Multiscale Finite Element Method ◽  
Multiscale Finite Element ◽  
Steady State Heat ◽  
Steady State Heat Transfer

In this paper, we present a new approach to model the steady-state heat transfer in heterogeneous materials. The multiscale finite element method (MsFEM) is improved and used to solve this problem. MsFEM is a fast and flexible method for upscaling. Its numerical efficiency is based on the natural parallelization of the main computations and their further simplifications due to the numerical nature of the problem. The approach does not require the distinct separation of scales, which makes its applicability to the numerical modeling of the composites very broad. Our novelty relies on modifications to the standard higher-order shape functions, which are then applied to the steady-state heat transfer problem. To the best of our knowledge, MsFEM (based on the special shape function assessment) has not been previously used for an approximation order higher than p = 2, with the hierarchical shape functions applied and non-periodic domains, in this problem. Some numerical results are presented and compared with the standard direct finite-element solutions. The first test shows the performance of higher-order MsFEM for the asphalt concrete sample which is subject to heating. The second test is the challenging problem of metal foam analysis. The thermal conductivity of air and aluminum differ by several orders of magnitude, which is typically very difficult for the upscaling methods. A very good agreement between our upscaled and reference results was observed, together with a significant reduction in the number of degrees of freedom. The error analysis and the p-convergence of the method are also presented. The latter is studied in terms of both the number of degrees of freedom and the computational time.

Some new results and current challenges in the finite element analysis of shells

Acta Numerica ◽  
2001 ◽  
Vol 10 ◽  
pp. 215-250 ◽  
Author(s):  
Dominique Chapelle
Keyword(s):  
Finite Element ◽  
Shell Theory ◽  
Shell Structures ◽  
Engineering Practice ◽  
Element Analysis ◽  
Shell Elements ◽  
Shell Models ◽  
The Finite Element Analysis ◽  
Shell Finite Element ◽  
Mathematical Analyses

This article, a companion to the article by Philippe G. Ciarlet on the mathematical modelling of shells also in this issue of Acta Numerica, focuses on numerical issues raised by the analysis of shells.Finite element procedures are widely used in engineering practice to analyse the behaviour of shell structures. However, the concept of ‘shell finite element’ is still somewhat fuzzy, as it may correspond to very different ideas and techniques in various actual implementations. In particular, a significant distinction can be made between shell elements that are obtained via the discretization of shell models, and shell elements – such as the general shell elements – derived from 3D formulations using some kinematic assumptions, without the use of any shell theory. Our first objective in this paper is to give a unified perspective of these two families of shell elements. This is expected to be very useful as it paves the way for further thorough mathematical analyses of shell elements. A particularly important motivation for this is the understanding and treatment of the deficiencies associated with the analysis of thin shells (among which is the locking phenomenon). We then survey these deficiencies, in the framework of the asymptotic behaviour of shell models. We conclude the article by giving some detailed guidelines to numerically assess the performance of shell finite elements when faced with these pathological phenomena, which is essential for the design of improved procedures.

Numerical Solution of a Wave Propagation Problem Along Plate Structures Based on the Isogeometric Approach

2018 ◽  
Vol 26 (01) ◽  
pp. 1750030 ◽  
Author(s):  
V. Hernández ◽  
J. Estrada ◽  
E. Moreno ◽  
S. Rodríguez ◽  
A. Mansur
Keyword(s):  
Degrees Of Freedom ◽  
Eigenvalue Problems ◽  
Computational Cost ◽  
Dispersion Curves ◽  
Wave Number ◽  
Spline Functions ◽  
Shape Functions ◽  
B Spline ◽  
Generalized Eigenvalue ◽  
Generalized Eigenvalue Problems

Ultrasonic guided waves propagating along large structures have great potential as a nondestructive evaluation method. In this context, it is very important to obtain the dispersion curves, which depend on the cross-section of the structure. In this paper, we compute dispersion curves along infinite isotropic plate-like structures using the semi-analytical method (SAFEM) with an isogeometric approach based on B-spline functions. The SAFEM method leads to a family of generalized eigenvalue problems depending on the wave number. For a prescribed wave number, the solution of this problem consists of the nodal displacement vector and the frequency of the guided wave. In this work, the results obtained with B-splines shape functions are compared to the numerical SAFEM solution with quadratic Lagrange shape functions. Advantages of the isogeometric approach are highlighted and include the smoothness of the displacement field components and the computational cost of solving the corresponding generalized eigenvalue problems. Finally, we investigate the convergence of Lagrange and B-spline approaches when the number of degrees of freedom grows. The study shows that cubic B-spline functions provide the best solution with the smallest relative errors for a given number of degrees of freedom.

A Multi-Mode Approach for the Nonlinear Vibrations of Circular Cylindrical Shells

2001 ◽  
Author(s):  
Francesco Pellicano ◽  
Marco Amabili ◽  
Michael P. Païdoussis
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Vibrations ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Nonlinear Behavior ◽  
Symbolic Manipulation ◽  
Comparison Functions ◽  
Circular Cylindrical Shells ◽  
Multi Mode

Abstract The nonlinear vibrations of simply supported, circular cylindrical shells, having geometric nonlinearities is analyzed. Donnell’s nonlinear shallow-shell theory is used, and the partial differential equations are spatially discretized by means of the Galerkin procedure, using a large number of degrees of freedom. A symbolic manipulation code is developed for the discretization, allowing an unlimited number of modes. In the displacement expansion particular care is given to the comparison functions in order to reduce as much as possible the dimension of the dynamical system, without losing accuracy. Both driven and companion modes are included, allowing for traveling-wave response of the shell. The fundamental role of the axisymmetric modes, which are included in the expansion, is confirmed and a convergence analysis is performed. The effect of the geometric shell characteristics, radius, length and thickness, on the nonlinear behavior is analyzed.

Turbulence-Induced Vibration Analysis of an Open Curved Thin Shell

2010 ◽  
Author(s):  
Mitra Esmailzadeh ◽  
Aouni A. Lakis
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Root Mean Square ◽  
Thin Shell ◽  
Shell Theory ◽  
Pressure Field ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Cross Spectral Density ◽  
Thin Shell Theory

A method is presented to predict the root mean square displacement response of an open curved thin shell structure subjected to a turbulent boundary-layer-induced random pressure field. The basic formulation of the dynamic problem is an efficient approach combining classic thin shell theory and the finite element method. The displacement functions are derived from Sanders’ thin shell theory. A numerical approach is proposed to obtain the total root mean square displacements of the structure in terms of the cross-spectral density of random pressure fields. The cross-spectral density of pressure fluctuations in the turbulent pressure field is described using the Corcos formulation. Exact integrations over surface and frequency lead to an expression for the total root mean square displacement response in terms of the characteristics of the structure and flow. An in-house program based on the presented method was developed. The total root mean square displacements of a curved thin blade subjected to turbulent boundary layers were calculated and illustrated as a function of free stream velocity and damping ratio. A numerical implementation for the vibration of a cylinder excited by fully developed turbulent boundary layer flow was presented. The results compared favorably with those obtained using software developed by Lakis et al.

Collapse of Thin Orthotropic Elliptical Cylindrical Shells Under Combined Bending and Pressure Loads

1979 ◽  
Vol 46 (2) ◽  
pp. 363-371 ◽  
Author(s):  
J. Spence ◽  
S. L. Toh
Keyword(s):  
Shell Theory ◽  
Nonlinear Boundary ◽  
Cylindrical Shells ◽  
Normal Pressure ◽  
Nonlinear Ordinary Differential Equations ◽  
Pure Bending ◽  
Finite Deflection ◽  
Shooting Technique ◽  
Theoretical Predictions ◽  
Thin Shell Theory

The elastic collapse of thin orthotropic elliptical cylindrical shells subject to pure bending alone or combined bending and uniform normal pressure loads has been studied. Nonlinear finite deflection thin shell theory is employed and this reduces the problem to a set of nonlinear ordinary differential equations. The resulting two-point nonlinear boundary-value problem is then linearized, using quasi-linearization, and solved numerically by the “shooting technique.” Some experimental work has been carried out and the results are compared with the theoretical predictions.

scholarly journals Three-dimensional stress analysis for beam-like structures using Serendipity Lagrange shape functions

2018 ◽  
Vol 141-142 ◽  
pp. 279-296 ◽  
Author(s):  
S. Minera ◽  
M. Patni ◽  
E. Carrera ◽  
M. Petrolo ◽  
P.M. Weaver ◽  
...  
Keyword(s):  
Stress Analysis ◽  
Three Dimensional ◽  
Shape Functions

TRANSIENT HEAT CONDUCTION IN FUNCTIONALLY GRADED MATERIALS

2007 ◽  
Vol 04 (04) ◽  
pp. 603-619 ◽  
Author(s):  
S. M. HAMZA-CHERIF ◽  
A. HOUMAT ◽  
A. HADJOUI
Keyword(s):  
Heat Conduction ◽  
Temperature Distribution ◽  
Functionally Graded Materials ◽  
Degrees Of Freedom ◽  
Functionally Graded ◽  
P Element ◽  
Transient Temperature ◽  
Test Problems ◽  
Shape Functions ◽  
Graded Materials

The h-p version of the finite element method (FEM) is considered to determine the transient temperature distribution in functionally graded materials (FGM). The h-p version may be regarded as the marriage of conventional h-version and p-version. The graded Fourier p-element is used to set up the two-dimensional heat conduction equations. The temperature is formulated in terms of linear shape functions used generally in FEM plus a variable number of trigonometric shape functions representing the internal degrees of freedom (DOF). In the graded Fourier p-element, the function of the thermal conductivity is computed exactly within the conductance matrix and thus overcomes the computational errors caused by the space discretization introduced by the FEM. Explicit and easily programmed trigonometric enriched capacitance, conductance matrices and heat load vectors are derived for plates and cylinders by using symbolic computation. The convergence properties of the h-p version proposed and the results of the numbers of test problems are in good agreement with the analytical solutions. Also, the effect of the non-homogeneity of the FGM on the temperature distribution is considered.

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