scholarly journals Thermal Buckling of Angle-Ply Laminated Plates Using New Displacement Function

2019 ◽  
Vol 25 (12) ◽  
pp. 96-113
Author(s):  
Ibtehal Abbas Sadiq ◽  
Widad Majeed
Keyword(s):  
Displacement Field ◽  
Equations Of Motion ◽  
Order Theory ◽  
Higher Order ◽  
Displacement Function ◽  
Thermal Buckling ◽  
Laminated Plates ◽  
Three Dimensions ◽  
Thin Plates ◽  
Aspect Ratios

ABSTRACT Critical buckling temperature of angle-ply laminated plate is developed using a higher-order displacement field. This displacement field used by Mantari et al based on a constant ‘‘m’’, which is determined to give results closest to the three dimensions elasticity (3-D) theory. Equations of motion based on higher-order theory angle ply plates are derived through Hamilton, s principle, and solved using Navier-type solution to obtain critical buckling temperature for simply supported laminated plates. Changing (α2/ α1) ratios, number of layers, aspect ratios, E1/E2 ratios for thick and thin plates and their effect on thermal buckling of angle-ply laminates are studied in detail. It is concluded that, this displacement field produces numerical results close to 3-D elasticity theory with maximum discrepancy (7.4 %).

scholarly journals Thermal buckling analysis of cross-ply plates based on new displacement field

2021 ◽  
Vol 9 (3B) ◽  
Author(s):  
Widad Ibraheem Majeed ◽  
Keyword(s):  
Elasticity Theory ◽  
Displacement Field ◽  
Equations Of Motion ◽  
Composite Plates ◽  
Thermal Buckling ◽  
Thin Plates ◽  
Aspect Ratios ◽  
Number Of Layers ◽  
3D Elasticity ◽  
Transverse Shear Strains

A higher-order displacement field is used for the analysis of the thermal buckling of composite plates subjected to thermal load; it is based on a constant ‘‘m’’, which is optimized to get results relatively close to those given by 3D elasticity theory. Adequate transverse shear strains distribution through the thickness and free stress surfaces of the plate is satisfied using this theory. Hamilton’s principle is used to derive equations of motion, which are solved using Navier-type series for simply supported plates. Thermal buckling of cross-ply laminates with various (α2 / α1) ratios, number of layers, aspect ratios, E1/E2 ratios, and stacking sequence for thick and thin plates is studied in detail. It is concluded that the obtained results using this displacement field are close to those calculated by 3D elasticity theory and other shear deformation plate theories when m=0.05.

Thermal buckling load optimization of laminated general quadrilateral and trapezoidal thin plates

2013 ◽  
Vol 20 (1) ◽  
pp. 87-94 ◽  
Author(s):  
Umut Topal
Keyword(s):  
Plate Theory ◽  
Mathematical Formulation ◽  
Thermal Buckling ◽  
Laminated Plates ◽  
Buckling Load ◽  
Thin Plates ◽  
Load Optimization ◽  
Aspect Ratios ◽  
Feasible Direction Method ◽  
Optimization Routine

AbstractThis paper deals with thermal buckling load optimization of symmetrically laminated angle-ply general quadrilateral and trapezoidal thin plates. The objective function is to maximize the critical temperature capacity of the quadrilateral and trapezoidal laminated plates and the fiber orientation is considered as a design variable. The mathematical formulation is based on the classical laminated plate theory for the frequency analysis. The modified feasible direction method is used as the optimization routine. Therefore, a program based on FORTRAN is used. Finally, the significant effects of aspect ratios, boundary conditions, taper ratios and unsymmetric trapezoidal plates on the optimal results are investigated and the results are compared.

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.

Generalized FVDAM Theory for Periodic Materials Undergoing Finite Deformations—Part II: Results

2013 ◽  
Vol 81 (2) ◽  
Author(s):  
Marcio A. A. Cavalcante ◽  
Marek-Jerzy Pindera
Keyword(s):  
Displacement Field ◽  
Computer Code ◽  
Biological Tissues ◽  
Order Theory ◽  
Substantial Improvement ◽  
Higher Order ◽  
Finite Deformations ◽  
Stress Distributions ◽  
Field Representation ◽  
Periodic Materials

In Part I, a generalized finite-volume direct averaging micromechanics (FVDAM) theory was constructed for periodic materials with complex microstructures undergoing finite deformations. The generalization involves the use of a higher-order displacement field representation within individual subvolumes of a discretized analysis domain whose coefficients were expressed in terms of surface-averaged kinematic variables required to be continuous across adjacent subvolume faces. In Part II of this contribution we demonstrate that the higher-order displacement representation leads to a substantial improvement in subvolume interfacial conformability and smoother stress distributions relative to the original theory based on a quadratic displacement field representation, herein called the 0th order theory. This improvement is particularly important in the finite-deformation domain wherein large differences in adjacent subvolume face rotations may lead to the loss of mesh integrity. The advantages of the generalized theory are illustrated through examples based on a known analytical solution and finite-element results generated with a computer code that mimics the generalized theory's framework. An application of the generalized FVDAM theory involving the response of wavy multilayers confirms previously generated results with the 0th order theory that revealed microstructural effects in this class of materials which are important in bio-inspired material architectures that mimic certain biological tissues.

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