A Quasi-Greens Function Method for the Bending Problem of Simply Supported Polygonal Shallow Spherical Shells on Pasternak Foundation

2013 ◽  
Vol 353-356 ◽  
pp. 3215-3219
Author(s):  
Shan Qing Li ◽  
Hong Yuan
Keyword(s):  
Function Method ◽  
Homogeneous Boundary Condition ◽  
Fredholm Integral Equations ◽  
Pasternak Foundation ◽  
Boundary Equation ◽  
Spherical Shells ◽  
Simply Supported ◽  
Suitable Form ◽  
Greens Function ◽  
Good Agreement

The quasi-Greens function method (QGFM) is applied to solve the bending problem of simply supported polygonal shallow spherical shells on Pasternak foundation. A quasi-Greens function is established by using the fundamental solution and the boundary equation of the problem. And the function satisfies the homogeneous boundary condition of the problem. Then the differential equation of the problem is reduced to two simultaneous Fredholm integral equations of the second kind by the Greens formula. The singularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The comparison with the ANSYS finite element solution shows a good agreement, and it demonstrates the feasibility and efficiency of the proposed method.

Application of the R-Function Theory for the Bending Problem of Shallow Spherical Shells with a Dodecagon Domain

2012 ◽  
Vol 468-471 ◽  
pp. 8-12 ◽  
Author(s):  
Shan Qing Li ◽  
Hong Yuan
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Theory ◽  
Homogeneous Boundary Condition ◽  
Fredholm Integral Equations ◽  
Winkler Foundation ◽  
Boundary Equation ◽  
Spherical Shells ◽  
Suitable Form ◽  
Good Agreement

The R-function theory is applied to describe the dodecagon domain of shallow spherical shells on Winkler foundation, and it is also used to construct a quasi-Green’s function. The quasi-Green’s function satisfies the homogeneous boundary condition of the problem. Then the differential equation of the problem is reduced to two simultaneous Fredholm integral equations of the second kind by the Green’s formula. The singularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. A comparison with the ANSYS finite element solution shows a good agreement, and it demonstrates the feasibility and efficiency of the present method.

A Quasi-Green’s Function Method for the Bending Problem of Simply Supported Trapezoidal Shallow Spherical Shells on Winkler Foundation

2012 ◽  
Vol 446-449 ◽  
pp. 3582-3586 ◽  
Author(s):  
Shan Qing Li ◽  
Hong Yuan
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Homogeneous Boundary Condition ◽  
Fredholm Integral Equations ◽  
Winkler Foundation ◽  
Boundary Equation ◽  
Spherical Shells ◽  
Green’S Function Method ◽  
Simply Supported

The quasi-Green’s function method (QGFM) is applied to solve the bending problem of simply supported trapezoidal shallow spherical shells on Winkler foundation. A quasi-Green’s function is established by using the fundamental solution and the boundary equation of the problem. And the function satisfies the homogeneous boundary condition of the problem. Then the differential equation of the problem is reduced to two simultaneous Fredholm integral equations of the second kind by the Green’s formula. The singularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The comparison with the ANSYS finite element solution shows a good agreement, and it demonstrates the feasibility and efficiency of the proposed method.

A Quasi-Green Function Method for Free Vibration of Clamped Orthotropic Parallelogram Thin Plates on Winkler Foundation

2013 ◽  
Vol 397-400 ◽  
pp. 431-434
Author(s):  
Shan Qing Li ◽  
Hong Yuan
Keyword(s):  
Integral Equation ◽  
Green Function ◽  
Free Vibration ◽  
Function Method ◽  
Homogeneous Boundary Condition ◽  
Thin Plates ◽  
Winkler Foundation ◽  
Boundary Equation ◽  
Green Function Method ◽  
Suitable Form

The quasi-Green function method (QGFM) is applied to solve the free vibration of clamped orthotropic thin plates with parallelogram boundary shape on Winkler foundation. Firstly the model governing differential equation of the problem is reduced to the boundary value problem of the biharmonic operator, and then it is reduced to the Fredholm integral equation of the second kind by Greens formula. A quasi-Green function is established by using the fundamental solution and the boundary equation of the problem. This function satisfies the homogeneous boundary condition of the problem. The singularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The comparison with ANSYS finite element solution shows a good agreement. The proposed method is a novel and effective mathematical one.

Green Quasifunction Method for Bending Problem of Clamped Orthotropic Trapezoidal Thin Plates on Winkler Foundation

2011 ◽  
Vol 138-139 ◽  
pp. 705-708 ◽  
Author(s):  
Shan Qing Li ◽  
Hong Yuan
Keyword(s):  
Integral Equation ◽  
Homogeneous Boundary Condition ◽  
Thin Plates ◽  
Winkler Foundation ◽  
Element Solution ◽  
Biharmonic Operator ◽  
Boundary Equation ◽  
Governing Differential Equation ◽  
Suitable Form ◽  
Good Agreement

The Green quasifunction method (GQM) is applied to solve the bending problem of clamped orthotropic thin plates with trapezoidal boundary shape on Winkler foundation. Firstly the governing differential equation of the problem is reduced to the boundary value problem of the biharmonic operator, and then it is reduced to the Fredholm integral equation of the second kind by Green’s formula. A Green quasifunction is established by using the fundamental solution and the boundary equation of the problem. This function satisfies the homogeneous boundary condition of the problem. The singularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The comparison with ANSYS finite element solution shows good agreement. The proposed method is a novel and effective mathematical one.

Green Quasifunction Method for Bending Problem of Clamped Orthotropic Thin Plates with Trapezoidal Boundary Shape

2011 ◽  
Vol 117-119 ◽  
pp. 456-459 ◽  
Author(s):  
Shan Qing Li ◽  
Hong Yuan
Keyword(s):  
Differential Equation ◽  
Mathematical Method ◽  
Integral Equation ◽  
Homogeneous Boundary Condition ◽  
Thin Plates ◽  
Biharmonic Operator ◽  
Boundary Equation ◽  
Boundary Shape ◽  
Governing Differential Equation ◽  
Suitable Form

The Green quasifunction method(GQM) is employed to solve the bending problem of clamped orthotropic thin plates with trapezoidal boundary shape. Firstly the governing differential equation of the problem is reduced to the boundary value problem of the biharmonic operator, and then it is reduced to the Fredholm integral equation of the second kind by Green’s formula. A Green quasifunction is established by using the fundamental solution and the boundary equation of the problem. This function satisfies the homogeneous boundary condition of the problem. The irregularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. A numerical example demonstrates the feasibility and efficiency of the proposed method, and it is a novel mathematical method.

Limit Pressures of Cylindrical and Spherical Shells

2000 ◽  
Vol 123 (3) ◽  
pp. 288-292 ◽  
Author(s):  
Arturs Kalnins ◽  
Dean P. Updike
Keyword(s):  
Geometric Parameter ◽  
Cylindrical Shells ◽  
Length Effect ◽  
Spherical Shells ◽  
Simply Supported ◽  
Limit Pressure ◽  
Section Viii ◽  
Division 2

Tresca limit pressures for long cylindrical shells and complete spherical shells subjected to arbitrary pressure, and several approximations to the exact limit pressures for limited pressure ranges, are derived. The results are compared with those in Section III-Subsection NB and in Section VIII-Division 2 of the ASME B&PV Code. It is found that in Section VIII-Division 2 the formulas agree with the derived limit pressures and their approximations, but that in Section III-Subsection NB the formula for spherical shells is different from the derived approximation to the limit pressure. The length effect on the limit pressure is investigated for cylindrical shells with simply supported ends. A geometric parameter that expresses the length effect is determined. A formula and its limit of validity are derived for an assessment of the length effect on the limit pressures.

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