scholarly journals Three-dimensional Stress Analysis of a Rectangular Cantilever Plate Using an Extended Love's Moderately Thick Plate Theory

1982 ◽  
Vol 25 (203) ◽  
pp. 720-727
Author(s):  
Michiaki KOBAYASHI ◽  
Toru NAGASAWA ◽  
Hiromasa ISHIKAWA ◽  
Kin-ichi HATA
Keyword(s):  
Stress Analysis ◽  
Thick Plate ◽  
Plate Theory ◽  
Three Dimensional ◽  
Cantilever Plate ◽  
Moderately Thick Plate

Failure behavior of hierarchical corrugated sandwich structures with second-order core based on Mindlin plate theory

2017 ◽  
Vol 21 (2) ◽  
pp. 552-579 ◽  
Author(s):  
Gang Li ◽  
Zhaokai Li ◽  
Peng Hao ◽  
Yutian Wang ◽  
Yaochu Fang
Keyword(s):  
Thick Plate ◽  
Failure Modes ◽  
Sandwich Structures ◽  
Plate Theory ◽  
Second Order ◽  
Mindlin Plate ◽  
Failure Behavior ◽  
Plate Model ◽  
Moderately Thick Plate ◽  
Mindlin Plate Theory

For hierarchical corrugated sandwich structures with second-order core, the prediction error of failure behavior by existing methods becomes unacceptable with the increase of structure thickness. In this study, a novel analytical model called moderately thick plate model is developed based on Mindlin plate theory, which can be used to analyze the failure behavior of hierarchical corrugated structures with second-order core under compression or shear loads. Then, the analytical expressions of nominal stress for six competing failure modes are derived based on the moderately thick plate model. The results of six different unit structures based on the moderately thick plate model agree quite well the ones by finite element methods. Furthermore, the influence of different structure thicknesses is investigated to validate the applicability of the moderately thick plate model. According to the comparative results with the thin plate model, the proposed moderately thick plate model has a better precision with the increase of the ratio of thickness to width for failure components.

scholarly journals A higher order triangular plate finite element using Airy functions

2020 ◽  
Vol 12 (11) ◽  
pp. 168781402097190
Author(s):  
Mohammed Himeur ◽  
Hamza Guenfoud ◽  
Mohamed Guenfoud
Keyword(s):  
Finite Element ◽  
Transverse Shear ◽  
Thick Plate ◽  
Plate Theory ◽  
Thin Plates ◽  
Airy Functions ◽  
Triangular Finite Element ◽  
Patch Tests ◽  
Moderately Thick Plate ◽  
Transverse Shear Locking

The present paper describes the formulation of a new moderately thick plate bending triangular finite element based on Mindlin–Reissner plate theory. It is called a Great Triangular Moderately Thick Plate Finite Element, or GTMTPFE. The formulation is based on the strain approach, on solution of Airy’s function and on the analytical integration in the construction of the stiffness matrix. The strengths associated with this approach consist of: • automatic verification of equilibrium conditions and kinematic compatibility conditions, • the enrichment of the degrees of the interpolation polynomials of displacements, strains and constraints (refinement p), • the consideration distortions sections related to Poisson effects, • the treatment of blocking phenomena related to transverse shear. In general, this approach results in a competitive, robust and efficient new moderately thick plate finite element. This is visible, on the one hand, through its stability against patch tests (constant twists, state of constants moments, transverse shear locking phenomenon, isotropy test). This is visible, through its good response to the patch tests to which it is subjected (constant torsions, state of constant moments, phenomenon of blocking in transverse shears, isotropy test). As has excellent convergence to the reference solution. Thus, it exhibits better performance behavior than other existing plate elements in the literature, particularly for moderately thick plates and for thin plates (L/h ratio greater than 4).

scholarly journals Analytical Study of Bending Characteristics of an Elastic Rectangular Plate using Direct Variational Energy Approach with Trigonometric Function

2021 ◽  
Vol 5 (6) ◽  
pp. 916-928
Author(s):  
F. C. Onyeka ◽  
B. O. Mama
Keyword(s):  
Deformation Theory ◽  
Thick Plate ◽  
Plate Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Energy Functional ◽  
Total Potential Energy ◽  
Total Potential ◽  
Plate Analysis ◽  
Potential Energy Functional

In this paper, an analytical three-dimensional (3D) bending characteristic of an isotropic rectangular thick plate with all edges simply supported (SSSS) and carrying uniformly distributed transverse load using the energy technique is presented. The three-dimensional constitutive relations which involves six stress components were used in the established, refined shear deformation theory to obtain a total potential energy functional. This theory obviates application of the shear correction factors for the solution to the problem. The governing equation of a thick plate was obtained by minimizing the total potential energy functional with respect to the out of plane displacement. The deflection functions which are in form of trigonometric were obtained as the solution of the governing equation. These deflection functions which are the product of the coefficient of deflection and shape function of the plate were substituted back into the energy functional, thereafter a realistic formula for calculating the deflection and stresses were obtained through minimizations with respect to the rotations and deflection coefficients. The values of the deflections and stresses obtained herein were tabulated and compared with those of previous 3D plate theory, refined plate theories and, classical plate theory (CPT) accordingly. It was observed that the result obtained herein varied more with those of CPT and RPT by 25.39% and 21.09% for all span-to-thickness ratios respectively. Meanwhile, the recorded percentage differences are as close as 7.17% for all span-to-thickness ratios, when compared with three dimensional plate analysis. This showed that exact 3D plate theory is more reliable than the shear deformation theory which are quite coarse for thick plate analysis. Doi: 10.28991/esj-2021-01320 Full Text: PDF

Conforming shear-locking-free four-node rectangular finite element of moderately thick plate

2016 ◽  
Vol 25 (5-6) ◽  
pp. 141-152
Author(s):  
Ivo Senjanović ◽  
Marko Tomić ◽  
Smiljko Rudan ◽  
Neven Hadžić
Keyword(s):  
Finite Element ◽  
Thick Plate ◽  
Plate Theory ◽  
Shear Stiffness ◽  
Mindlin Plate ◽  
Shear Locking ◽  
Shape Functions ◽  
Beam Shape ◽  
Stiffness Matrices ◽  
Moderately Thick Plate

AbstractAn outline of the modified Mindlin plate theory, which deals with bending deflection as a single variable, is presented. Shear deflection and cross-section rotation angles are functions of bending deflection. A new four-node rectangular finite element of moderately thick plate is formulated by utilizing the modified Mindlin theory. Shape functions of total (bending+shear) deflections are defined as a product of the Timshenko beam shape functions in the plate longitudinal and transversal direction. The bending and shear stiffness matrices, and translational and rotary mass matrices are specified. In this way conforming and shear-locking-free finite element is obtained. Numerical examples of plate vibration analysis, performed for various combinations of boundary conditions, show high level of accuracy and monotonic convergence of natural frequencies to analytical values. The new finite element is superior to some sophisticated finite elements incorporated in commercial software.

scholarly journals Nonlinear Vibrations of Laminated Cross-Ply Composite Cantilever Plate in Subsonic Air Flow

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Gen Liu ◽  
Wei Zhang ◽  
An Xi
Keyword(s):  
Differential Equations ◽  
Finite Length ◽  
Nonlinear Vibrations ◽  
Aerodynamic Force ◽  
Plate Theory ◽  
Air Flow ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Cantilever Plate ◽  
Partial Differential

The nonlinear vibrations and responses of a laminated composite cantilever plate under the subsonic air flow are investigated in this paper. The subsonic air flow around the three-dimensional cantilever rectangle laminated composite plate is considered to be decreasing from the wing root to the wing tip. According to the ideal incompressible fluid flow condition and the Kutta–Joukowski lift theorem, the subsonic aerodynamic lift on the three-dimensional finite length flat wing is calculated by using the Vortex Lattice (VL) method. The finite length flat wing is modeled as a laminated composite cantilever plate based on Reddy’s third-order shear deformation plate theory and the von Karman geometry nonlinearity is introduced. The nonlinear partial differential governing equations of motion for the laminated composite cantilever plate subjected to the subsonic aerodynamic force are established via Hamilton’s principle. The Galerkin method is used to separate the partial differential equations into two nonlinear ordinary differential equations, and the four-dimensional nonlinear averaged equations are obtained by the multiple scale method. Through comparing the natural frequencies of the linear system with different material and geometric parameters, the relationship of 1 : 2 internal resonance is considered. Corresponding to several selected parameters, the frequency-response curves are obtained. The hardening-spring-type behaviors and jump phenomena are exhibited. The influence of the force excitation on the bifurcations and chaotic behaviors of the laminated composite cantilever plate is investigated numerically. It is found that the system is sensitive to the exciting force according to the complicate nonlinear behaviors exhibited in this paper.

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