Nonlinear Axisymmetric Static Analysis of Shallow Spherical Shells on Winkler-Pasternak Foundation

1987 ◽  
Vol 109 (1) ◽  
pp. 28-34 ◽  
Author(s):  
R. K. Jain ◽  
Y. Nath
Keyword(s):  
Static Analysis ◽  
Nonlinear Static Analysis ◽  
Normal Displacement ◽  
Pasternak Foundation ◽  
Chebyshev Series ◽  
Circular Plates ◽  
Spherical Shells ◽  
Linear Elastic ◽  
Annular Plates ◽  
Edge Conditions

In the present investigation nonlinear static analysis of thin axisymmetric circular plates, annular plates and shallow spherical shells resting on linear elastic Winkler-Pasternak foundation under uniformly distributed normal loads, has been carried out. Donnell-type governing differential equations expressed in terms of normal displacement and stress function have been employed and solved using Chebyshev series. A convergence study for Chebyshev series has been conducted. The influence of foundation stiffness parameters (K and G) on the response of circular plates, annulus and spherical shells has been studied for both the clamped and simply supported immovable edge conditions. A few typical snap-through results for shells are also included.

Semi-Analytical Solution for Functionally Graded Solid Circular and Annular Plates Resting on Elastic Foundations Subjected to Axisymmetric Transverse Loading

2012 ◽  
Vol 4 (2) ◽  
pp. 205-222 ◽  
Author(s):  
A. Behravan Rad
Keyword(s):  
Elastic Foundation ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
Circular Plates ◽  
Linear Elastic ◽  
Edge Conditions ◽  
The One ◽  
Foundation Plate

AbstractIn this paper, the static analysis of functionally graded (FG) circular plates resting on linear elastic foundation with various edge conditions is carried out by using a semi-analytical approach. The governing differential equations are derived based on the three dimensional theory of elasticity and assuming that the mechanical properties of the material vary exponentially along the thickness direction and Poisson’s ratio remains constant. The solution is obtained by employing the state space method (SSM) to express exactly the plate behavior along the graded direction and the one dimensional differential quadrature method (DQM) to approximate the radial variations of the parameters. The effects of different parameters (e.g., material property gradient index, elastic foundation coefficients, the surfaces conditions (hard or soft surface of the plate on foundation), plate geometric parameters and edges condition) on the deformation and stress distributions of the FG circular plates are investigated.

Nonlinear Static Analysis of Orthotropic Piezoelectric Shallow Cylindrical Shell on Elastic Foundation

2006 ◽  
Author(s):  
K. M. Gupta ◽  
Sandeep Kumar
Keyword(s):  
Cylindrical Shell ◽  
Differential Equations ◽  
Static Analysis ◽  
Constitutive Relations ◽  
Nonlinear Static Analysis ◽  
Geometrical Parameters ◽  
Pasternak Foundation ◽  
Shallow Cylindrical Shell ◽  
Minimization Technique ◽  
Nonlinear Static

With growth and emergence in the field of adaptive materials, the need arises to study their applications in the field of structural, aerodynamic, aerospace and other fields. These materials can be used as sensors, transducers, and actuators. Although their basic constitutive relations are already developed, but there is still a great deal of scope left in the field of applications. With this aim, a nonlinear static analysis of orthotropic piezoelectric shallow cylindrical shell on Pasternak foundation is investigated in the present work. Basic formulation of the problem is based on strain energy concept, and the governing differential equations are obtained by using Euler’s variational principle. Galerkin error minimization technique has been used to solve the governing differential equations. The results are presented for simply supported immovable edge boundary condition. Influences of shell geometry, foundation parameter, and piezoelectric properties on load-deflection characteristics for different radius-to-thickness ratios are studied. Numerical results have been obtained for different values of geometrical parameters in terms of load, displacement, and electric potential. Geometrical parameters are represented through non-dimensional entities η = a2/Rh, λ = Ka4/D11, and μ = Ga2/D11. The results are compared with nonlinear static analysis of an orthotropic shallow cylindrical shell without piezoelectric layer on Pasternak foundation. It is observed that an increase in the value of piezoelectric constant decreases the deflection of the shallow cylindrical shell under the identical values.

Axisymmetric Nonlinear Dynamic Response of Bimodulus Annular Plates

1990 ◽  
Vol 112 (2) ◽  
pp. 202-205
Author(s):  
R. S. Srinivasan ◽  
L. S. Ramachandra
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Geometrically Nonlinear ◽  
Circular Plates ◽  
Governing Equations ◽  
Numerical Work ◽  
Nonlinear Dynamic Response ◽  
Annular Plates ◽  
Edge Conditions ◽  
The Time Domain

In the present study, the geometrically nonlinear dynamic response of bimodulus annular and circular plates is obtained. The governing equations of the problem are formulated using the energy method and are solved by using annular finite elements spacewise. The integration in the time domain is accomplished by the Wilson θ method. Numerical work has been done for different hole sizes under various edge conditions and loadings.

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.

Bending of Thin Ring-Sector Plates

1951 ◽  
Vol 18 (4) ◽  
pp. 359-363
Author(s):  
L. I. Deverall ◽  
C. J. Thorne
Keyword(s):  
Continuous Function ◽  
Bending Moment ◽  
Circular Ring ◽  
Circular Plates ◽  
Thin Ring ◽  
Special Cases ◽  
Edge Conditions

Abstract General expressions for the deflection of plates whose planform is a sector of a circular ring are given for cases in which the straight edges have arbitrary but given deflection and bending moment. The solutions are given for all combinations of physically important edge conditions on the two circular edges. Sectors of circular plates are included as special cases. Solutions are given for a general load which is a continuous function of r, and a sectionally continuous function of θ, where r and θ are the usual polar co-ordinates with the pole at the center of the ring. Several specific examples are given.

Pushover Analysis Based on Equivalent Diagonal Springs for the Assessment of the Seismic Safety of Post-and-Beam Timber Buildings Braced with Nailed Shear Walls

2017 ◽  
Vol 755 ◽  
pp. 170-180
Author(s):  
Natalino Gattesco ◽  
Ingrid Boem
Keyword(s):  
Static Analysis ◽  
Pushover Analysis ◽  
Shear Walls ◽  
Nonlinear Static Analysis ◽  
Plastic Behavior ◽  
Ground Acceleration ◽  
Good Reliability ◽  
Equivalent Viscous Damping ◽  
Seismic Safety ◽  
Capacity Spectrum

A method for a simplified modeling of post-and-beam timber buildings braced with nailed shear walls, useful for seismic design purposes, is presented and discussed in the paper. This strategy is based on the schematization of the vertical diaphragms through equivalent diagonal springs with elastic-plastic behavior and allows the assessment of the resisting ground acceleration by performing nonlinear static analysis; the Capacity Spectrum method based on equivalent viscous damping was applied. This nonlinear procedure constitutes a reliable and simple alternative to the linear static analysis using the behavior factor q. The procedures to determine the characteristics of the equivalent elements (stiffness and load-carrying capacity) are based on analytical evaluations, starting from the actual characteristic of shear walls. A comparison between the results of numerical simulation based of more refined and complex models, previously presented by the authors, and this time-reducing, simplified analysis proved the good reliability of the method.

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