The Bending Singularity at the Apex of V-Notch in an Anisotropic Thick Plate

2017 ◽  
Vol 735 ◽  
pp. 95-99
Author(s):  
Chung De Chen
Keyword(s):  
Eigenfunction Expansion ◽  
Thick Plate ◽  
Plate Theory ◽  
Expansion Method ◽  
Numerical Results ◽  
The Other ◽  
Mindlin Plate ◽  
Eigenfunction Expansion Method ◽  
Singularity Order ◽  
Mindlin Plate Theory

In this paper, the bending singularity at the apex of V-notch in an anisotropic thick plate is investigated. The Stroh-like formalism is used to model the anisotropy of the material. Based on the Ressiner-Mindlin plate theory and the eigenfunction expansion method, the characteristic equation for bending singularity order is derived and the order can be determined numerically. The numerical results show that the singularity orders strongly depend on the plate angle a. In addition, the singularity orders also depend on the principal orientation of the anisotropic material. The singularity orders for the case of are stronger than for that of. In the case of, to reduce the anisotropy is helpful to release the singularity at the notch tip. For the other case of, it is preferable to increase the anisotropy to reduce the singularity. The disappearance conditions of the bending singularity can be found based on the numerical results.

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.

An Eigenfunction Expansion Method in the Stress Concentration Analysis

2012 ◽  
Vol 204-208 ◽  
pp. 4406-4409
Author(s):  
Yang Bai ◽  
Li Chen
Keyword(s):  
Stress Concentration ◽  
Boundary Conditions ◽  
Linear Combination ◽  
Eigenfunction Expansion ◽  
Original Problem ◽  
Expansion Method ◽  
Numerical Results ◽  
Eigenfunction Expansion Method ◽  
Completeness Property

This paper deals with the traditional stress concentration problems based on the eigenfunction expansion approach. Due to the completeness property of the eigenfunction space obtained by the previous researches, the solution of an arbitrary problem can be expressed by their linear combination. Thus the original problem is transformed into finding the combination of these eigenfuctions satisfying boundary conditions. By applying adjoint symplectic relationships of the ortho-normalization, the combination can be obtained numerically. Numerical results in tensional problems show that stress concentration appears when one of the ends of the solid is clamped. The concentration is seriously confined near the boundary of the fixed, and decrease rapidly with the distance of the boundarys.

scholarly journals Investigations of Bending Singularity Orders in a V-notched Composite Laminate Plate Based on the Ressiner-Mindlin Theory

2018 ◽  
Vol 151 ◽  
pp. 01001
Author(s):  
Chung-De Chen
Keyword(s):  
Eigenfunction Expansion ◽  
Composite Laminate ◽  
Laminate Plate ◽  
Expansion Method ◽  
Material Anisotropy ◽  
Free Surfaces ◽  
Eigenfunction Expansion Method ◽  
Composite Laminate Plate ◽  
Material Orientation ◽  
Singularity Order

In this paper, the bending singularity at the apex of a V-notched composite laminate plate is investigated. The anisotropy of the laminate is modeled by the Stroh formalism. Based on the eigenfunction expansion method, the bending singularity orders can be determined by solving an eigenvalue problem numerically. The singularity orders depend on the plate angle, material orientation, material anisotropy and the laminate stacking sequence. The comparison cases show that the material orientation should avoid in order to reduce the bending singularity. The layers near the free surfaces have more significant effects on the singularity order. The findings presented in this paper are helpful in the design of the composite laminate with V-notch.

Wave Interaction With Floating Elastic Plate Based on the Timoshenko–Mindlin Plate Theory

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
K. M. Praveen ◽  
D. Karmakar ◽  
C. Guedes Soares
Keyword(s):  
Dispersion Relation ◽  
Elastic Plate ◽  
Plate Theory ◽  
Wave Interaction ◽  
Bending Moment ◽  
Expansion Method ◽  
Wave Theory ◽  
Mindlin Plate ◽  
Floating Elastic Plate ◽  
Mindlin Plate Theory

In the present study, the wave interaction with the very large floating structures (VLFSs) is analyzed considering the small amplitude wave theory. The VLFS is modeled as a 2D floating elastic plate with infinite width based on Timoshenko–Mindlin plate theory. The eigenfunction expansion method along with mode-coupling relation is used to analyze the hydroelastic behavior of VLFSs in finite water depth. The contour plots for the plate covered dispersion relation are presented to illustrate the complexity in the roots of the dispersion relation. The wave scattering behavior in the form of reflection and transmission coefficients are studied in detail. The hydroelastic performance of the elastic plate interacting with the ocean wave is analyzed for deflection, strain, bending moment, and shear force along the elastic plate. Further, the study is extended for shallow water approximation, and the results are compared for both Timoshenko–Mindlin plate theory and Kirchhoff’s plate theory. The significance and importance of rotary inertia and shear deformation in analyzing the hydroelastic characteristics of VLFSs are presented. The study will be helpful for scientists and engineers in the design and analysis of the VLFSs.

ACCURATE FREQUENCIES AND MODE SHAPES FOR MODERATELY THICK, CANTILEVERED, SKEW PLATES

2007 ◽  
Vol 07 (03) ◽  
pp. 425-440 ◽  
Author(s):  
A. W. LEISSA ◽  
C. S. HUANG ◽  
M. J. CHANG
Keyword(s):  
Plate Theory ◽  
Ritz Method ◽  
The Other ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Transverse Displacement ◽  
Algebraic Polynomials ◽  
Stress Singularities ◽  
Dependent Variables ◽  
Mindlin Plate Theory

Accurate free vibration frequencies and mode shapes are presented for complete sets of moderately thick, cantilevered skew plates of triangular, trapezoidal and parallelogram shape. These accurate results are obtained by using the Ritz method applied to the Mindlin plate theory. Two sets of functions are employed simultaneously for each of the three dependent variables: transverse displacement (w) and bending rotations (ϕx and ϕy). One set is the widely used algebraic polynomials. The other is the set of corner functions which provide the proper stress singularities in the reentrant clamped-free corner, and accelerates the convergence of the solutions. The extensive frequencies presented are exact to the four digits shown. Corresponding mode shapes are also shown, by means of nodal patterns, most of which are novel in the published literature.

The Quasi-Static Analysis for Two-Dimensional Thin Plates

2011 ◽  
Vol 255-260 ◽  
pp. 166-169
Author(s):  
Li Chen ◽  
Yang Bai
Keyword(s):  
Boundary Conditions ◽  
Eigenfunction Expansion ◽  
Solution Space ◽  
Expansion Method ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Elastic Plates ◽  
Various Boundary Conditions ◽  
Eigenfunction Expansion Method ◽  
Concentration Phenomena

The eigenfunction expansion method is introduced into the numerical calculations of elastic plates. Based on the variational method, all the fundamental solutions of the governing equations are obtained directly. Using eigenfunction expansion method, various boundary conditions can be conveniently described by the combination of the eigenfunctions due to the completeness of the solution space. The coefficients of the combination are determined by the boundary conditions. In the numerical example, the stress concentration phenomena produced by the restriction of displacement conditions is discussed in detail.

Coupled Extensional and Flexural Motions of a Two-Layer Plate With Interface Slip

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Peng Li ◽  
Feng Jin ◽  
Weiqiu Chen ◽  
Jiashi Yang
Keyword(s):  
Plate Theory ◽  
Cutoff Frequency ◽  
Great Influence ◽  
Imperfect Interface ◽  
Mindlin Plate ◽  
Finite Plate ◽  
Mindlin Plate Theory ◽  
Interface Elasticity ◽  
Propagating Shear ◽  
Perfect Interface

The effect of imperfect interface on the coupled extensional and flexural motions in a two-layer elastic plate is investigated from views of theoretical analysis and numerical simulations. A set of full two-dimensional equations is obtained based on Mindlin plate theory and shear-slip model, which concerns the interface elasticity and tangential discontinuous displacements across the bonding imperfect interface. Some numerical examples are processed, including the propagation of straight-crested waves in an unbounded plate, the buckling of a finite plate, as well as the deflection of a finite plate under uniform load. It is revealed that the bending-evanescent wave in the composites with a perfect interface eventually cuts-on to a propagating shear-like wave with cutoff frequency when the two sublayers imperfectly bonded. The similar phenomenon has been verified once again for coupled face-shear and thickness-shear waves. It also has been pointed out that the interfacial parameter has a great influence on the performance of static buckling, in which the outcome can be reduced to classical buckling load of a simply supported plate when the interface is perfect.

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