A Thin Shell Theoretical Solution for Two Intersecting Cylindrical Shells Due to External Branch Pipe Moments

2004 ◽  
Author(s):  
M. D. Xue ◽  
D. F. Li ◽  
K. C. Hwang
Keyword(s):  
Thin Shell ◽  
Cylindrical Shells ◽  
Branch Pipe ◽  
Three Dimensional ◽  
Homogeneous Solution ◽  
Displacement Function ◽  
Theoretical Solution ◽  
External Branch ◽  
Particular Solution ◽  
Good Agreement

Two intersecting cylindrical shells subjected to internal pressure and external moment are of common occurrence in pressure vessel and piping industry. The highest stress intensity occurring in the vicinity of junction, which is a complex space curve when the diameter ratio d/D increases. As the new process of theoretical solution and design criteria research developed by the authors, the stress analysis based on the theory of thin shell is carried out for cylindrical shells with normally intersecting nozzles subjected to three kinds of external branch pipe moments. The thin shell theoretical solution for the main shell with cutout, on which a moment is applied, is obtained by superposing a particular solution on the homogeneous solution. The double trigonometric series solution of cylindrical shell subjected to arbitrary distributed normal and tangential forces based on Timoshenko equation is used for the particular solution and the Xue et al.’s solution, for the homogeneous solution based on the modified Morley equation instead of the Donnell shallow shell equation. The displacement function solution for the nozzle with a nonplanar end is obtained on the basis of the Goldenveizer equation instead of Timoshenko’s. The presented results are in good agreement with those obtained by experiments and by three-dimensional finite element method. The present analytical results are in good agreement with WRC Bulletin 297 when d/D is small. The theoretical solution can be applied to d/D ≤ 0.8, λ = d/DT ≤ 8 and d/D ≤ t/T ≤ 2 successfully.

A Thin Shell Theoretical Solution for Two Intersecting Cylindrical Shells Due to External Branch Pipe Moments

2005 ◽  
Vol 127 (4) ◽  
pp. 357-368 ◽  
Author(s):  
M. D. Xue ◽  
D. F. Li ◽  
K. C. Hwang
Keyword(s):  
Cylindrical Shells ◽  
Branch Pipe ◽  
Homogeneous Solution ◽  
Theoretical Solution ◽  
Intersection Curve ◽  
3D Fem ◽  
External Branch ◽  
Particular Solution ◽  
Shell Equation ◽  
Distributed Forces

A theoretical solution is presented for cylindrical shells with normally intersecting nozzles subjected to three kinds of external branch pipe moments. The improved double trigonometric series solution is used for the particular solution of main shell subjected to distributed forces, and the modified Morley equation instead of the Donnell shallow shell equation is used for the homogeneous solution of the shell with cutout. The Goldenveizer equation instead of Timoshenko’s is used for the nozzle with a nonplanar end. The accurate continuity conditions at the intersection curve are adopted instead of approximate ones. The presented results are in good agreement with those obtained by tests and by 3D FEM and with WRC Bulletin 297 when d∕D is small. The theoretical solution can be applied to d∕D⩽0.8, λ=d∕DT⩽8, and d∕D⩽t∕T⩽2 successfully.

A Stress Analysis Method for Cylindrical Shells With Nozzles Subjected to Internal Pressure, External Forces and Moments

2006 ◽  
Author(s):  
Ming-De Xue ◽  
Qing-Hai Du ◽  
Dong-Feng Li ◽  
Keh-Chih Hwang
Keyword(s):  
Internal Pressure ◽  
Stress Analysis ◽  
Thin Shell ◽  
Cylindrical Shells ◽  
Branch Pipe ◽  
Three Dimensional ◽  
Theoretical Solution ◽  
Analysis Method ◽  
External Forces ◽  
Three Dimensional Finite Element

An identical stress analysis method based on the thin shell theory is carried out for cylindrical shells with normally intersecting nozzles subjected to internal pressure and six kinds of external branch pipe loads involving axial tension, two kinds of transverse shear forces, longitudinal and circumferential bending and torsion moments. The thin shell theoretical solution is obtained based on the Morley equation instead of the Donnell shallow shell equation. The accurate continuity conditions at the intersecting curve, which is a complicated space curve, are adopted. The presented results are verified by three-dimensional finite element method (FEM). The theoretical solution can be applied to d/D ≤ 0.8, λ = d/DT ≤ 12 and d/D ≤ t/T ≤ 2 successfully. The solutions are in good agreement with WRC Bulletin 297 when diameter ratio is small. In the paper some typical design curves calculated by the theoretical solutions are presented and their applicable ranges are greatly expanded in comparison with current design methods.

Stress analysis of cylindrical shells with nozzles due to external run pipe moments

2000 ◽  
Vol 35 (3) ◽  
pp. 159-170 ◽  
Author(s):  
M. D Xue ◽  
H. H Wang ◽  
K. C Hwang
Keyword(s):  
Thin Shell ◽  
Cylindrical Shells ◽  
Large Diameter ◽  
Three Dimensional ◽  
Diameter Ratio ◽  
Test Results ◽  
Present Solution ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element ◽  
Good Agreement

In this paper the analytical results of two normally intersecting cylindrical shells subjected to external moments on the ends of main shells are presented. The thin shell theoretical solutions are obtained on the basis of the modified Morley equation for the main shell with a cut out with large diameter ratio and of the Goldenveizer equation for the branch tube with a nonplaner end. The results are in good agreement with the previous test results and with Moffat's three-dimensional finite element method results. The design curves based on the present solution can be applied to d/D ≤ 0.8 successfully.

An Analytical Method for Cylindrical Shells With Nozzles Due to Internal Pressure and External Loads—Part I: Theoretical Foundation

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Ming-De Xue ◽  
Qing-Hai Du ◽  
Keh-Chih Hwang ◽  
Zhi-Hai Xiang
Keyword(s):  
Analytical Solution ◽  
Internal Pressure ◽  
Stress Analysis ◽  
Pressure Vessel ◽  
Cylindrical Shells ◽  
Branch Pipe ◽  
Theoretical Solution ◽  
External Branch ◽  
Complex Valued ◽  
External Loads

An improved version of the analytical solutions by Xue, Hwang and co-workers (1991, “Some Results on Analytical Solution of Cylindrical Shells With Large Opening,” ASME J. Pressure Vessel Technol., 113, 297–307; 1991, “The Stress Analysis of Cylindrical Shells With Rigid Inclusions Having a Large Ratio of Radii,” SMiRT 11 Transactions F, F05/2, 85–90; 1995, “The Thin Theoretical Solution for Cylindrical Shells With Large Openings,” Acta Mech. Sin., 27(4), pp. 482–488; 1995, “Stresses at the Intersection of Two Cylindrical Shells,” Nucl. Eng. Des., 154, 231–238; 1996, “A Reinforcement Design Method Based on Analysis of Large Openings in Cylindrical Pressure Vessels,” ASME J. Pressure Vessel Technol., 118, 502–506; 1999, “Analytical Solution for Cylindrical Thin Shells With Normally Intersecting Nozzles Due to External Moments on the Ends of Shells,” Sci. China, Ser. A: Math., Phys., Astron., 42(3), 293–304; 2000, “Stress Analysis of Cylindrical Shells With Nozzles Due to External Run Pipe Moments,” J. Strain Anal. Eng. Des., 35, 159–170; 2004, “Analytical Solution of Two Intersecting Cylindrical Shells Subjected to Transverse Moment on Nozzle,” Int. J. Solids Struct., 41(24–25), 6949–6962; 2005, “A Thin Shell Theoretical Solution for Two Intersecting Cylindrical Shells Due to External Branch Pipe Moments,” ASME J. Pressure Vessel Technol., 127(4), 357–368; 2005, “Theoretical Stress Analysis of Two Intersecting Cylindrical Shells Subjected to External Loads Transmitted Through Branch Pipes,” Int. J. Solids Struct., 42, 3299–3319) for two normally intersecting cylindrical shells is presented, and the applicable ranges of the theoretical solutions are successfully extended from d/D≤0.8 and λ=d/(DT)1/2≤8 to d/D≤0.9 and λ≤12. The thin shell theoretical solution is obtained by solving a complex boundary value problem for a pair of fourth-order complex-valued partial differential equations (exact Morley equations (Morley, 1959, “An Improvement on Donnell’s Approximation for Thin Walled Circular Cylinders,” Q. J. Mech. Appl. Math. 12, 89–91; Simmonds, 1966, “A Set of Simple, Accurate Equations for Circular Cylindrical Elastic Shells,” Int. J. Solids Struct., 2, 525–541)) for the shell and the nozzle. The accuracy of results is improved by some additional terms to the expressions for resultant forces and moments in terms of complex-valued displacement-stress function. The theoretical stress concentration factors due to internal pressure obtained by the improved expressions are in agreement with previously published test results. The theoretical results discussed and presented herein are in sufficient agreement with those obtained from three dimensional finite element analyses for all the seven load cases, i.e., internal pressure and six external branch pipe load components involving three orthogonal forces and the respective three orthogonal moments.

Fast Solution of Three-Dimensional Modified Helmholtz Equations by the Method of Fundamental Solutions

2016 ◽  
Vol 20 (2) ◽  
pp. 512-533 ◽  
Author(s):  
Ji Lin ◽  
C. S. Chen ◽  
Chein-Shan Liu
Keyword(s):  
Three Dimensional ◽  
Homogeneous Solution ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Singular Problem ◽  
Helmholtz Equations ◽  
Particular Solutions ◽  
Radial Basis ◽  
Particular Solution ◽  
Polyharmonic Spline

AbstractThis paper describes an application of the recently developed sparse scheme of the method of fundamental solutions (MFS) for the simulation of three-dimensional modified Helmholtz problems. The solution to the given problems is approximated by a two-step strategy which consists of evaluating the particular solution and the homogeneous solution. The homogeneous solution is approximated by the traditional MFS. The original dense system of the MFS formulation is condensed into a sparse system based on the exponential decay of the fundamental solutions. Hence, the homogeneous solution can be efficiently obtained. The method of particular solutions with polyharmonic spline radial basis functions and the localized method of approximate particular solutions in combination with the Gaussian radial basis function are employed to approximate the particular solution. Three numerical examples including a near singular problem are presented to show the simplicity and effectiveness of this approach.

FREE VIBRATIONS OF COMBINED HEMISPHERICAL–CYLINDRICAL SHELLS OF REVOLUTION WITH A TOP OPENING

2013 ◽  
Vol 14 (01) ◽  
pp. 1350023 ◽  
Author(s):  
JAE-HOON KANG
Keyword(s):  
Present Method ◽  
Thin Shell ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Ritz Method ◽  
Three Dimensional ◽  
Free Vibrations ◽  
Two Dimensional ◽  
Algebraic Polynomials ◽  
Shells Of Revolution

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies of joined hemispherical–cylindrical shells of revolution with a top opening. 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, uθ and uz in the radial, circumferential, and axial directions, respectively, are taken to be periodic in θ and in time, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the joined shells are formulated, and 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. Natural frequencies are presented for different boundary conditions. The frequencies from the present 3D method are compared with those from 2D thin shell theories.

scholarly journals Three-Dimensional Vibration Analysis of Isotropic and Orthotropic Open Shells and Plates with Arbitrary Boundary Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-29 ◽  
Author(s):  
Guoyong Jin ◽  
Tiangui Ye ◽  
Shuangxia Shi
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Cylindrical Shells ◽  
Three Dimensional ◽  
Displacement Function ◽  
Rectangular Plates ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Open Shells ◽  
Benchmark Solutions

This paper presents elasticity solutions for the vibration analysis of isotropic and orthotropic open shells and plates with arbitrary boundary conditions, including spherical and cylindrical shells and rectangular plates. Vibration characteristics of the shells and plates have been obtained via a unified three-dimensional displacement-based energy formulation represented in the general shell coordinates, in which the displacement in each direction is expanded as a triplicate product of the cosine Fourier series with the addition of certain supplementary terms introduced to eliminate any possible jumps with the original displacement function and its relevant derivatives at the boundaries. All the expansion coefficients are then treated equally as independent generalized coordinates and determined by the Rayleigh-Ritz procedure. To validate the accuracy of the present method and the corresponding theoretical formulations, numerical cases have been compared against the results in the literature and those of 3D FE analysis, with excellent agreements obtained. The effects of boundary conditions, material parameters, and geometric dimensions on the frequencies are discussed as well. Finally, several 3D vibration results of isotropic and orthotropic open spherical and cylindrical shells and plates with different geometry dimensions are presented for various boundary conditions, which may be served as benchmark solutions for future researchers as well as structure designers in this field.

Analysis of Transient Bioheat Transfer in the Human Eye Using Hybrid Finite Element Model

2014 ◽  
Vol 553 ◽  
pp. 356-361 ◽  
Author(s):  
Ze Wei Zhang ◽  
Hui Wang ◽  
Qing Hua Qin
Keyword(s):  
Finite Element ◽  
Homogeneous Solution ◽  
Element Model ◽  
Bioheat Transfer ◽  
Bioheat Equation ◽  
Human Eye ◽  
Time Stepping ◽  
Hybrid Finite Element ◽  
Particular Solution ◽  
Good Agreement

Simulation of transient bioheat transfer in a two dimensional (2D) human eye model is conducted using a newly developed hybrid fundamental solution-finite element method (HFS-FEM) coupling with the radial basis function (RBF) approximation. Firstly, a time stepping scheme based on the finite difference method (FDM) is used to handle time variable in the transient Pennes bioheat equation. Secondly, the particular solution of the governing equation is approximated by a RBF approach. Then, the homogeneous solution is calculated by means of HFS-FEM. The obtained results are compared with those from ABAQUS and a good agreement between them is observed.

A Universal Design Method Based on Analysis for Cylindrical Shells With Nozzles Due to Internal Pressure, External Forces and Moments: Part I

2009 ◽  
Author(s):  
Ming-De Xue ◽  
Qing-Hai Du ◽  
Keh-Chih Hwang ◽  
Zhi-Hai Xiang
Keyword(s):  
Internal Pressure ◽  
Design Method ◽  
Cylindrical Shells ◽  
Branch Pipe ◽  
External Branch ◽  
Complex Boundary ◽  
Stress Concentration Factors ◽  
Accuracy Of Results ◽  
External Forces ◽  
Complex Valued

An improved version is presented for analytical solution developed by the authors and the applicable ranges of the theoretical solutions for two normally intersecting cylindrical shells are successfully extended from d/D≤0.8 and λ=d/(DT)1/2≤8 up to d/D ≤0.9 and λ≤12. The thin shell theoretical solution is obtained by solving a complex boundary value problem for a pair of 4-th order complex-valued partial differential equations (exact Morley equations) for the shell and the nozzle. The accuracy of results is improved by some additional terms to the expressions for resultant forces and moments in terms of complex-valued displacement-stress function. The presented theoretical stress concentration factors due to pressure are in agreement with the test results in literatures. The presented theoretical results are in good agreement with those by 3-D finite element method for all the seven load cases, i.e., internal pressure and six external branch pipe load components involving axial tension, two kinds of transverse shear forces, longitudinal and circumferential bending and torsion moments.

A Free Energy Perturbation Approach to Estimate the Intrinsic Solubilities of Drug-like Small Molecules

2019 ◽  
Author(s):  
Sayan Mondal ◽  
Gary Tresadern ◽  
Jeremy Greenwood ◽  
Byungchan Kim ◽  
Joe Kaus ◽  
...  
Keyword(s):  
Solid State ◽  
Small Molecules ◽  
Three Dimensional ◽  
Aqueous Solubility ◽  
Computational Approach ◽  
Free Energy Perturbation ◽  
Perturbation Approach ◽  
Energy Perturbation ◽  
State Form ◽  
Good Agreement

<p>Optimizing the solubility of small molecules is important in a wide variety of contexts, including in drug discovery where the optimization of aqueous solubility is often crucial to achieve oral bioavailability. In such a context, solubility optimization cannot be successfully pursued by indiscriminate increases in polarity, which would likely reduce permeability and potency. Moreover, increasing polarity may not even improve solubility itself in many cases, if it stabilizes the solid-state form. Here we present a novel physics-based approach to predict the solubility of small molecules, that takes into account three-dimensional solid-state characteristics in addition to polarity. The calculated solubilities are in good agreement with experimental solubilities taken both from the literature as well as from several active pharmaceutical discovery projects. This computational approach enables strategies to optimize solubility by disrupting the three-dimensional solid-state packing of novel chemical matter, illustrated here for an active medicinal chemistry campaign.</p>

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