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1
Content available remote A sub-parametric shear deformable element for free vibration analysis of thick/thin rectangular plates with tapered thickness
Manna M. C.
International Journal of Applied Mechanics and Engineering
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2006
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Vol. 11, no 4
901-913
EN
A sub-parametric shear deformable element is proposed for free vibration analysis of isotropic plates with linearly varying thickness in one direction. The element has sixteen nodes and thirty-six degrees of freedom. The transverse displacement and bending rotations are taken as independent field variables. The polynomials used to express these variables are of the same order. The geometry of the element is defined by a polynomial of lower order than the polynomials used for field variables. The entire formulation is made based on first-order shear deformation theory (FSDT). The rotary inertia is included in the consistent mass matrix for the analysis. Isotropic plates with different thickness ratios (varying from 0.01 to 0.2), tapered ratios, aspect ratios and boundary conditions are analyzed. The results obtained by the present element show an excellent agreement with the available published results. Some numerical results have been given as new results.
2
Content available remote A new high-precision triangular plate element
Manna M. C.
International Journal of Applied Mechanics and Engineering
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2004
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Vol. 9, no 2
361-382
EN
This paper deals with the development of a new triangular finite element for bending analysis of isotropic rectangular plates by an explicit stiffness matrix. The first order shear deformation theory (FOSDT) is used to include the effect of transverse shear deformation. The element has eighteen nodes on the sides and six internal nodes. The geometry of the element is expressed by three linear shape functions of area coordinates. The formulation is displacement type and the use of area coordinates makes the shape functions for field variables to be expressed explicitly. No numerical integration is required to get the element stiffness matrix. The element has fifty-one degrees of freedom, which can be reduced to thirty-nine degrees of freedom by a standard static condensation of the degrees of freedom associated with the internal nodes. An interesting feature of the element is that it is not prone to shear locking. Numerical examples are presented to show the accuracy and convergence characteristics of the element.
3
Content available remote Static analysis of isotropic thick/thin skew plates by finite element method
Haldar S., Manna M. C., Sheikih A. H.
International Journal of Applied Mechanics and Engineering
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2003
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Vol. 8, no 2
245-254
EN
A general first order shear deformation theory has been developed to analyze the bending behavior of isotropic skew plates. The plates having different skew angles ('alpha'), aspect ratios (a/b), boundary conditions and transverse loading conditions (concentrated load, uniformly distributed load, hydrostatic varying load and sinusoidal varying load) have been analyzed by the nine node isoparametric element. The analysis has also been performed considering plate thickness ratio varying from a/b=0.001 to a/b=0.02. The deflections and principal bending moments in non-dimensional forms have been presented at different locations of the plates. The present solutions have been compared with the published results wherever available and have got good agreement. Some numerical solutions have been given which may be treated as new results.
4
Content available remote Free vibration of isotropic thick/thin plates using a sub-parametric shear deformable element
Manna M. C., Haldar S., Sheikh A. H.
International Journal of Applied Mechanics and Engineering
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2003
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Vol. 8, no 3
441-448
EN
A free vibration analysis of isotropic plates is investigated in this paper. A sixteen node sub-parametric element having thirty-six degrees of freedom is developed for this purpose. The transverse displacement and bending rotations are taken as independent field variables. The polynomials used to express these variables are of the same order. The entire formulation is made based on the first-order shear deformation theory (FSDT). The rotary inertia is included in the consistent mass matrix for the analysis. Isotropic plates with different thickness ratios, aspect ratios and boundary conditions are analyzed. The results show an excellent agreement with the available published analytical results.
5
Content available remote Bending analysis of isotropic plates using a sixteen-noded sub-parametric element
Manna M. C., Haldar S., Bhattacharya A. K.
International Journal of Applied Mechanics and Engineering
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2002
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Vol. 7, no 4
1279-1290
EN
Static analysis of isotropic plates under uniformly distributed and point loading is investigated in this paper. A sixteen noded sub-parametric element having fifty-two degrees of freedom is developed for this purpose. The first order shear deformation theory (FSDT) has been used in the entire analysis. The transverse and in-plane displacements and bending rotations are taken as independent field variables and the polynomials used to express these variables are of different orders.
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