scholarly journals Enforcement Techinque of Essential Bounary Conditions for Nonlinear Plate Bending Problem employing Reproducing Kernel Approximation

2012 ◽  
Vol 68 (2) ◽  
pp. I_249-I_260
Author(s):  
Shota SADAMOTO ◽  
Satoyuki TANAKA ◽  
Shigenobu OKAZAWA
Keyword(s):  
Reproducing Kernel ◽  
Plate Bending ◽  
Kernel Approximation ◽  
Nonlinear Plate ◽  
Plate Bending Problem

NONLINEAR THIN-PLATE BENDING ANALYSES USING THE HERMITE REPRODUCING KERNEL APPROXIMATION

2012 ◽  
Vol 09 (01) ◽  
pp. 1240012 ◽  
Author(s):  
SATOYUKI TANAKA ◽  
SHOTA SADAMOTO ◽  
SHIGENOBU OKAZAWA
Keyword(s):  
Thin Plate ◽  
Reproducing Kernel ◽  
Geometrical Nonlinearity ◽  
Mathematical Formulation ◽  
Thin Plates ◽  
Plate Bending ◽  
Kernel Approximation ◽  
Hermite Reproducing Kernel Approximation ◽  
Lagrange Strain ◽  
Thin Plate Bending

This study analyzed thin-plate bending problems with a geometrical nonlinearity using the Hermite reproducing kernel approximation and sub-domain-stabilized conforming integration. In thin-plate bending analyses, the deflections and rotations satisfy so-called Kirchhoff mode reproducing conditions. It is then possible to solve large deflection analyses of thin plates, such as elastic bucking problems, with high accuracy and efficiency. Total Lagrangian method is applied to solve the geometrical nonlinearity of the thin plates' deflections and rotations. The Green–Lagrange strain and second Piola–Kirchhoff stress forms are adopted to represent the strains and stresses in the thin plates. Mathematical formulation and some numerical examples are also demonstrated.

scholarly journals Numerical Solution of the Kirchhoff Plate Bending Problem with BEM

2011 ◽  
Vol 2011 ◽  
pp. 1-14
Author(s):  
V. V. Zozulya
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Boundary Integral ◽  
Kirchhoff Plate ◽  
Reciprocal Theorem ◽  
Plate Bending ◽  
Linear Boundary ◽  
Analytical Formulas ◽  
Bending Problems ◽  
Plate Bending Problem

Direct approach based on Betty's reciprocal theorem is employed to obtain a general formulation of Kirchhoff plate bending problems in terms of the boundary integral equation (BIE) method. For spatial discretization a collocation method with linear boundary elements (BEs) is adopted. Analytical formulas for regular and divergent integrals calculation are presented. Numerical calculations that illustrate effectiveness of the proposed approach have been done.

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