Adhesion and delamination boundary conditions for elastic plates with arbitrary contact shape

2010 ◽  
Vol 37 (2) ◽  
pp. 214-218 ◽  
Author(s):  
Carmel Majidi ◽  
George G. Adams
Keyword(s):  
Boundary Conditions ◽  
Elastic Plates ◽  
Contact Shape

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.

Stability of Thin Elastic Plates Covering an Arbitrary Simply Connected Region and Subject to any Admissible Boundary Conditions

1953 ◽  
Vol 20 (1) ◽  
pp. 23-29
Author(s):  
G. A. Zizicas
Keyword(s):  
Boundary Conditions ◽  
Direct Method ◽  
Elastic Plates ◽  
Simple Manner ◽  
Particular Solutions ◽  
Isotropic Plates ◽  
Simply Connected Region ◽  
Simply Connected ◽  
A Direct Method ◽  
Thin Elastic Plates

Abstract The Bergman method of solving boundary-value problems by means of particular solutions of the differential equation, which are constructed without reference to the boundary conditions, is applied to the problem of stability of thin elastic plates of an arbitrary simply connected shape and subject to any admissible boundary conditions. A direct method is presented for the construction of particular solutions that is applicable to both anisotropic and isotropic plates. Previous results of M. Z. Krzywoblocki for isotropic plates are obtained in a simple manner.

scholarly journals Numerical solution of acoustic scattering by finite perforated elastic plates

2016 ◽  
Vol 472 (2188) ◽  
pp. 20150767 ◽  
Author(s):  
A. V. G. Cavalieri ◽  
W. R. Wolf ◽  
J. W. Jaworski
Keyword(s):  
Boundary Conditions ◽  
Acoustic Scattering ◽  
Free Edge ◽  
Solution Procedure ◽  
Sound Level ◽  
Vibration Modes ◽  
Elastic Plates ◽  
Beneficial Effects ◽  
Plate Length ◽  
Radiated Sound

We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k 0 based on the plate length. However, at low k 0 , finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k 0 . The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k 0 for perforated elastic plates.

Large-Amplitude Oscillations of Unsymmetrically Laminated Anisotropic Rectangular Plates Including Shear, Rotatory Inertia, and Transverse Normal Stress

1985 ◽  
Vol 52 (3) ◽  
pp. 536-542 ◽  
Author(s):  
K. S. Sivakumaran ◽  
C. Y. Chia
Keyword(s):  
Boundary Conditions ◽  
Normal Stress ◽  
Transverse Shear ◽  
Plate Theory ◽  
Orientation Angle ◽  
Nonlinear Frequency ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Rotatory Inertia ◽  
Transverse Normal Stress

This paper is concerned with nonlinear free vibrations of generally laminated anisotropic elastic plates. Based on Reissner’s variational principle a nonlinear plate theory is developed. The effects of transverse shear, rotatory inertia, transverse normal stress, and transverse normal contraction or extension are included in this theory. Using the Galerkin procedure and principle of harmonic balance, approximate solutions to governing equations of unsymmetrically laminated rectangular plates including transverse shear, rotatory inertia, and transverse normal stress are formulated for various boundary conditions. Numerical results for the ratio of nonlinear frequency to linear frequency of unsymmetric angle-ply and cross-ply laminates are presented graphically for various values of elastic properties, fiber orientation angle, number of layers, and aspect ratio and for different boundary conditions. Present results are also compared with available data.

scholarly journals Determining the Geometrical Sizes of Plates with Internal Hinges by Using Additional Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Vildan Yazıcı ◽  
Zahir Muradoğlu
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Transmission Conditions ◽  
Elastic Plates ◽  
Different Boundary Conditions ◽  
Mechanical Constraints ◽  
Finite Difference Equations ◽  
The Common

For a system obtained by placing more than two elastic plates side by side, the transmission conditions are obtained at the common boundaries. Finite difference equations are developed for the problem of plates with internal hinges and applied for determination of the response of a system assembled from three different plates with different mechanical constraints between adjacent plates in this study. An algorithm is written to find out how long the size of the plates should be in order to obtain the desired amount of bending against the force affecting the system under different boundary conditions. The bisection and multigrid methods are used for this. These two methods are compared based on the obtained data.

scholarly journals PARTIAL WAVE BASIS ADAPTED TO EXTERIOR BOUNDARY CONDITIONS OF AN ELASTIC PLATE

2021 ◽  
Vol 20 (1) ◽  
pp. 35-43
Author(s):  
Sergiu Cojocaru ◽  
Keyword(s):  
Boundary Conditions ◽  
Elastic Plate ◽  
Functional Form ◽  
Standard Treatment ◽  
Plane Waves ◽  
Equation Of Motion ◽  
Elastic Vibration ◽  
Vibration Modes ◽  
Elastic Plates ◽  
Partial Waves

An approach to describing normal elastic vibration modes in confined systems is presented. In a standard treatment of the problem, the displacement field is represented by a superposition of partial waves of a general form, e.g., plane waves. The unknown coefficients of superposition are then obtained from the equation of motion and the full set of boundary conditions. In the proposed approach, the functional form of partial waves is chosen in such a way as to satisfy the boundary conditions on exterior surfaces identically, i.e., even if the unknown quantities determined by the remaining constraints are found in an approximation, numerically or analytically. Some examples of solutions for composite elastic plates are discussed to illustrate the efficiency of the approach and its relevance for applications.

Influence Functions in the Numerical Analysis of Bending of Thin Elastic Plates

1984 ◽  
Vol 8 (2) ◽  
pp. 103-114 ◽  
Author(s):  
Mohammed F.N. Mohsen ◽  
Ali A. Al-Gadhib ◽  
Mohammed H. Baluch
Keyword(s):  
Boundary Conditions ◽  
Influence Function ◽  
Infinite Plate ◽  
Thin Plates ◽  
Influence Functions ◽  
Algebraic Equations ◽  
Elastic Plates ◽  
The Real ◽  
Linear Algebraic Equations ◽  
The Moment

A numerical method for the linear analysis of thin plates of arbitrary plan form and subjected to arbitrary loading and boundary conditions is presented in this paper. This method is an extension of the Wu-Altiero method [1] where use has been made of the force influence function for an infinite plate, whereas the work contained in this paper is based on the use of the moment influence function of an infinite plate. The technique basically involves embedding the real plate into a fictitious infinite plate for which the moment influence function is known. N points are prescribed at the plate boundary at which the boundary conditions for the original problem are collocated by means of 2N fictitious moments placed around contours outside the domain of the real plate. A system of 2N linear algebraic equations in the unknown moments is obtained. The solution of the system yields the unknown moments. These may in turn be used to compute deflection, moments or shear at any point in the thin plate. Finally, the method is extended to include influence functions of both concentrated forces and concentrated moments. This is obtained by applying concentrated moments and forces simultaneously on the contours located outside the domain of the plate.

scholarly journals Mixed boundary conditions in the relaxational treatment of biharmonic problems (plane strain or stress)

1947 ◽  
Vol 189 (1019) ◽  
pp. 535-543 ◽  
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Plane Strain ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Elastic Plates ◽  
Relaxation Methods ◽  
Valuable Alternative ◽  
Engineering Problems ◽  
Biharmonic Problems

Relaxation methods have already been applied to the solution of four problems of (i) extension and (ii) flexure of flat elastic plates, in which ( a ) displacement or ( b ) traction is specified at the boundary. Here the method is adapted to the case in which the two types of boundary condition are mixed, where photo-elastic methods are difficult to apply. Two examples are treated by relaxation methods, and the results obtained indicate that this method may be a valuable alternative in engineering problems.

Sign in / Sign up

Export Citation Format

Share Document