2003 ◽  
Vol 70 (2) ◽  
pp. 260-267 ◽  
Author(s):  
Z.-Q. Cheng ◽  
J. N. Reddy

This paper presents fundamental solutions of an anisotropic elastic thin plate within the context of the Kirchhoff theory. The plate material is inhomogeneous in the thickness direction. Two systems of problems with non-self-equilibrated loads are solved. The first is concerned with in-plane concentrated forces and moments and in-plane discontinuous displacements and slopes, and the second with transverse concentrated forces. Exact closed-form Green’s functions for infinite and semi-infinite plates are obtained using the recently established octet formalism by the authors for coupled stretching and bending deformations of a plate. The Green functions for an infinite plate and the surface Green functions for a semi-infinite plate are presented in a real form. The hoop stress resultants are also presented in a real form for a semi-infinite plate.


2003 ◽  
Vol 125 (1) ◽  
pp. 88-94 ◽  
Author(s):  
Manfred Nader ◽  
Hubert Gattringer ◽  
Michael Krommer ◽  
Hans Irschik

Vibrations of smart elastic plates with integrated piezoelectric actuators are considered. Piezoelastic layers are used to generate a distributed actuation of the plate. A spatial shape function of the piezoelastic actuators is sought such that flexural vibrations induced by external forces can be completely nullified. An analytic solution of this problem is worked out for the case of clamped circular plates with a spatially constant force loading. The Kirchhoff theory of thin plates is used to derive this analytic solution. Our result is successfully validated by means of coupled 3-dimensional finite-element computations.


Author(s):  
Mohammed Himeur ◽  
Mohamed Guenfoud

We present a new plate bending triangular finite element. It is developed in perspective to building shell elements. Its formulation uses concepts related to the deformation approach, the fourth fictitious node, the static condensation and analytic integration. It is based on the assumptions of the theory of thin plates (Kirchhoff theory). The approach has resulted in a bending plate finite element (HIMEUR) competitive, robust and efficient.


2013 ◽  
Vol 40 (4) ◽  
pp. 543-561
Author(s):  
Xu Wang ◽  
Peter Schiavone

A Stroh-like formalism is developed for the heat conduction and the coupled stretching and bending deformations of a laminated anisotropic thermoelastic thin plate based on Kirchhoff theory. For the heat conduction problem, a Stroh-like quartic formalism is developed. Twodimensional generalized temperature and heat flux function vectors are introduced. The structure of the introduced 4x4 fundamental plate matrix for heat conduction is the same as that of the 8x8 fundamental elasticity matrix in the Stroh sextic formalism for generalized plane strain elasticity. Consequently, the orthogonality and closure relations for heat conduction in thin plates is established. For the thermoelastic problem, an inhomogeneous particular solution is derived rigorously. We obtain an octet formalism in which the general solution is composed of the well-known homogeneous solution developed by Cheng and Reddy (isothermal case) and the inhomogeneous particular solution arising from the thermal effect.


1957 ◽  
Vol 24 (1) ◽  
pp. 115-121
Author(s):  
Osamu Tamate

Abstract In a previous paper by the author (1), a theoretical solution for an infinite strip with a circular hole under plain bending is given by the method of successive approximation. This method demands laborious calculations. However, it seems that the labor can be diminished by employing the method of perturbation. In this paper, the effect of a circular hole in an infinite strip under the state of pure twist is investigated with the help of the perturbation method. The maximum deflections on the rim of the hole and the maximum stress couples in the strip are calculated and plotted versus hole-diameter strip-width ratio and Poisson’s ratio of the plate material. Here the strip is considered subjected to the limitation of the Poisson-Kirchhoff theory of bending of thin plates.


1959 ◽  
Vol 26 (4) ◽  
pp. 661-665
Author(s):  
O. Tamate

Abstract The problem of finding stress resultants in a semi-infinite plate under plain bending and containing an infinite row of equal and equally spaced circular holes is discussed on the basis of the Poisson-Kirchhoff theory of thin plates. A method of perturbation is adopted for the determination of parametric coefficients included in the solution. The maximum bending moments occurring on the rim of the hole across the minimum section are calculated for several cases and shown in graphs, from which the mutual interference of adjacent boundaries will be informed.


1992 ◽  
Vol 4 (1) ◽  
pp. 127-138
Author(s):  
Masahiko Hirao ◽  
Hidekazu Fukuoka ◽  
Yoshinori Murakami
Keyword(s):  

Sign in / Sign up

Export Citation Format

Share Document