scholarly journals The asymptotic solution of the first dynamic boundary value problem of the theory of elasticity for two-layered orthotropic plate.

2011 ◽  
Vol 64 (2) ◽  
pp. 15-25
Author(s):  
L.A. Aghalovyan ◽  
T.V. Zakaryan
Keyword(s):  
Boundary Value Problem ◽  
Asymptotic Solution ◽  
Orthotropic Plate ◽  
Boundary Value ◽  
Theory Of Elasticity ◽  
Dynamic Boundary

scholarly journals The first boundary value problem of the dynamics of an anisotropic elastic half-space under the action of subsonic transport loads

2020 ◽  
Vol 4 (78) ◽  
pp. 45-52
Author(s):  
G. K. ZAKIR’YANOVA ◽  
◽  
L. A. ALEXEYEVA ◽  
Keyword(s):  
Rock Mass ◽  
Boundary Value Problem ◽  
Half Space ◽  
Wide Class ◽  
Boundary Value ◽  
Operator Method ◽  
Elastic Half Space ◽  
Theory Of Elasticity ◽  
Wide Range ◽  
Anisotropic Elastic

The first boundary value problem of the theory of elasticity for an anisotropic elastic half-space is solved when a transport load moves along its surface. The subsonic Raleigh case is considered, when the velocity of motion is less than the velocity of propagation of bulk and surface elastic waves. The Green’s tensor of the transport boundary value problem is constructed and on its basis the solution of boundary value problems for a wide class of distributed traffic loads is given. To solve the problem, the methods of tensor and linear algebra, integral Fourier transform, and operator method for solving systems of differential equations were used. The obtained solution makes it possible to investigate the dynamics of the rock mass for a wide class of transport loads, in a wide range of velocities, both low velocities and high velocities, and to evaluate the strength properties of the rock mass under the influence of road transport. In particular, determine the permissible velocities of its movement and carrying capacity. In addition, a investigation on its basis of the movement of the day surface along the route will make it possible to establish criteria for the seismic resistance of ground structures and the permissible distances of their location from the route.

Convergence of the Finite Element Method in the Theory of Elasticity

1968 ◽  
Vol 35 (2) ◽  
pp. 274-278 ◽  
Author(s):  
M. W. Johnson ◽  
R. W. McLay
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variational Principle ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Theory Of Elasticity ◽  
Careful Consideration ◽  
Stress Singularities ◽  
The Finite Element Method ◽  
Element Method

The foundations of the theory of the finite element method as it applies to linear elasticity are investigated. A particular boundary-value problem in plane stress is considered and the variational principle for the finite element method is shown to be equivalent to it. Mean and uniform convergence of the finite element solution to that of the boundary-value problem is demonstrated with careful consideration given to the stress singularities. A counterexample is presented in which a set of functions, admissible to the variational principle, is shown not to converge.

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