Analytical Bending Solutions of Orthotropic Rectangular Thin Plates with Two Adjacent Edges Free and the Others Clamped or Simply Supported Using Finite Integral Transform Method

Xu, Qinqin; Zhong, Yi; Ullah, Salamat; Zhang, Jinghui; Gao, Yuanyuan

doi:10.1155/2020/8848879

Cited by 4 publications

(4 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [62], the authors applied the finite integral transformation method to solve the flexural problems of rectangular Kirchhoff plates made with orthogonally anisotropic materials. They considered plates with two adjacent free boundaries and the other boundaries fixed or on simple suppports (FFCC or FFSS) plates.…”

Section: Review Of Solution Methods For Plate Problemsmentioning

confidence: 99%

Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

Ike¹,

Onyia²,

Rowland-Lato³

2021

Adv. sci. technol. eng. syst. j.

View full text Add to dashboard Cite

This paper presents the generalized integral transform method for solving flexural and elastic stability problems of rectangular thin plates clamped along /2 yb = and simply supported along remaining boundaries (x = 0, x = a) (CSCS plate). The considered plate is homogeneous, isotropic and carrying uniformly distributed transversely applied loading causing bending. Also studied, is a plate subject to (i) biaxial (ii) uniaxial uniform compressive load. The method uses the eigenfunctions of vibrating thin beams of equivalent span and support conditions in constructing the basis functions for the plate deflection and the integral kernel function. The transform is applied to the governing domain equation, converting the problem to integral equations for both cases of bending and elastic buckling. The integral equation reduces to algebraic problems for the bending problem, and algebraic eigenvalue problem for the elastic buckling problem. The deflections are obtained as double infinite series with rapidly convergent properties. Bending moments expressions are double series with infinite terms which are rapidly convergent. Maximum deflections and bending moments values occur at the plate centre in agreement with symmetry. The present results gave double series solutions with good convergent properties in closed form for bending problems. The resulting bending solutions were exact. Solving the resulting eigenvalue equation gave closed analytical equation for the buckling loads. Buckling loads are computed for the cases of biaxial and uniaxial uniform compression of square thin plates using one term approximations. The buckling load obtained for one term approximation of the eigenfunction gave results that are 12.23% greater than the exact solution. The use of more terms in the eigenfunction expansion could give more acceptable results for the eigenvalue problem of buckling of CSCS plates.

show abstract

Section: Review Of Solution Methods For Plate Problemsmentioning

confidence: 99%

Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

Ike¹,

Onyia²,

Rowland-Lato³

2021

Adv. sci. technol. eng. syst. j.

View full text Add to dashboard Cite

show abstract

“…The classical Kirchhoff-Love static plate bending problem assumes: (1) thin plate; (2) small deformation; and (3) constant thickness, etc. The problem can be expressed as the following governing differential equation [19]:…”

Section: A Classical Kirchhoff Plate Bending Theorymentioning

confidence: 99%

“…5) [24]. Unknown coefficients a j are solved by applying ϕ (x,y) to satisfy boundary conditions [19], [20].…”

Section: A Loading Conditionmentioning

confidence: 99%

A Computational Design and Evaluation Tool for 3D Structures with Planar Surfaces

Liu¹,

Yan²,

Moure³

et al. 2021

Preprint

View full text Add to dashboard Cite

Three dimensional (3D) structures composed of planar surfaces can be build out of accessible materials using easier fabrication technique with shorter fabrication time. To better design 3D structures with planar surfaces, realistic models are required to understand and evaluate mechanical behaviors. Existing design tools are either effort-consuming (e.g. finite element analysis) or bounded by assumptions (e.g. numerical solutions). In this project, We have built a computational design tool that is (1) capable of rapidly and inexpensively evaluating planar surfaces in 3D structures, with sufficient computational efficiency and accuracy; (2) applicable to complex boundary conditions and loading conditions, both isotropic materials and orthotropic materials; and (3) suitable for rapid accommodation when design parameters need to be adjusted. We demonstrate the efficiency and necessity of this design tool by evaluating a glass table as well as a wood bookcase, and iteratively designing an origami gripper to satisfy performance requirements. This design tool gives non-expert users as well as engineers a simple and effective modus operandi in structural design.

show abstract

“…The theory is based on a power series expansion of the displacement vector component in each layer for the transverse direction, where the number of terms retained in the power series is arbitrary and chosen according to the problem being considered. Xu et al [15] proposed analytical solutions for orthotropic thin plates, where the finite integral transform method was introduced for accurate bending analysis. This type of analysis is limited only to thin plates due to the Kirchhoff-Love plate theory applied to derive the employed method.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Bending Analysis of Multi-Layered Orthotropic Plates by Two-Dimensional Numerical Model

2021

View full text Add to dashboard Cite

The paper presents effective numerical modelling of multi-layered plates with orthotropic properties. The method called the FEM23 is employed to construct the numerical model. The approach enables a full 3D analysis to be performed while using a 2D finite element mesh. The numerical model for a multi-layered plate is constructed by an assembling procedure, where each layer with orthotropic properties is added to the global numerical model. The paper demonstrates that the FEM23 method is very flexible in defining the multilayered plate, where the thickness of each layer as well as its mechanical orthotropic properties can be defined independently. Several examples of three-layered or nine-layered plates are analyzed in this paper. The results obtained by the FEM23 method coincide with the ones taken from the published papers or calculated with the standard 3D FEM approach. The orthotropic version of the FEM23 can be quite easily applied for other kinds of problems including thermo-mechanics, free vibrations, buckling analysis, or delamination.

show abstract

Analytical Bending Solutions of Orthotropic Rectangular Thin Plates with Two Adjacent Edges Free and the Others Clamped or Simply Supported Using Finite Integral Transform Method

Cited by 4 publications

References 41 publications

Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

A Computational Design and Evaluation Tool for 3D Structures with Planar Surfaces

Three-Dimensional Bending Analysis of Multi-Layered Orthotropic Plates by Two-Dimensional Numerical Model

Contact Info

Product

Resources

About