An efficient higher-order theory and finite element for laminated plates subjected to thermal loading

2006 ◽  
Vol 73 (1) ◽  
pp. 99-109 ◽  
Author(s):  
Wu Zhen ◽  
Chen Wanji
Keyword(s):  
Finite Element ◽  
Thermal Loading ◽  
Order Theory ◽  
Higher Order ◽  
Laminated Plates ◽  
Higher Order Theory

A Consistent Higher-Order Theory of Laminated Plates with Nonlinear Impact Modal Analysis

1994 ◽  
Vol 116 (3) ◽  
pp. 371-378 ◽  
Author(s):  
C. C. Chao ◽  
T. P. Tung ◽  
C. C. Sheu ◽  
J. H. Tseng
Keyword(s):  
Modal Analysis ◽  
Double Fourier Series ◽  
Order Theory ◽  
Higher Order ◽  
Small Time ◽  
Laminated Plates ◽  
Surface And Interface ◽  
Higher Order Theory ◽  
Patch Loading ◽  
The Impact

A consistent higher-order theory is developed for cross-ply laminated thick plates under transverse normal impact via an energy variational approach, in which the 3-D surface/edge boundary conditions and interlaminar displacement/stress continuities are satisfied, in an attempt to find the dynamic deformation and all six stress components throughout the plate during the impact process. The dynamic displacement field is expressed in a mixed form of in-plane double Fourier series and cubic polynomials through thickness as 12 variables for each layer. A system of modified Lagrange’s equations is derived with all surface and interface constraints included. The nonlinear impact modal analysis is performed using the Hertz contact law in a patch loading simulation and Green’s function for small time-steps linearization. The 3-D displacements are found with thickness shrinking and stresses generally unsymmetric with respect to the mid-surface. Tensile cracks are predicted at the unimpacted side.

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