A Remarkable Tensor in Plane Linear Elasticity

1997 ◽  
Vol 64 (3) ◽  
pp. 704-707 ◽  
Author(s):  
Q.-C. He
Keyword(s):  
Boundary Value Problem ◽  
Linear Elasticity ◽  
Boundary Value ◽  
Symmetric Tensor ◽  
Two Dimensional ◽  
Symmetric Tensors ◽  
Elastic Tensor ◽  
Angle Rotation ◽  
Plane Linear Elasticity ◽  
The Right

It is shown that any two-dimensional elastic tensor can be orthogonally and uniquely decomposed into a symmetric tensor and an antisymmetric tensor. To within a scalar multiplier, the latter turns out to be equal to the right-angle rotation on the space of two-dimensional second-order symmetric tensors. On the basis of these facts, several useful results are derived for the traction boundary value problem of plane linear elasticity.

On the solution to a two-dimensional boundary value problem of heat conduction in a degenerating domain

2020 ◽  
Vol 98 (2) ◽  
pp. 100-109
Author(s):  
Minzilya T. Kosmakova ◽  
◽  
Valery G. Romanovski ◽  
Dana M. Akhmanova ◽  
Zhanar M. Tuleutaeva ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Two Dimensional ◽  
Dimensional Boundary

A Method for the Numerical Solution of a Boundary Value Problem for a Linear Differential Equation with Interval Parameters

2019 ◽  
Vol 16 (07) ◽  
pp. 1850115 ◽  
Author(s):  
Nizami A. Gasilov ◽  
Müjdat Kaya
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Linear Differential Equation ◽  
Numerical Method ◽  
Boundary Value ◽  
Real Life ◽  
Boundary Values ◽  
Right Hand ◽  
Linear Differential ◽  
The Right

In many real life applications, the behavior of the system is modeled by a boundary value problem (BVP) for a linear differential equation. If the uncertainties in the boundary values, the right-hand side function and the coefficient functions are to be taken into account, then in many cases an interval boundary value problem (IBVP) arises. In this study, for such an IBVP, we propose a different approach than the ones in common use. In the investigated IBVP, the boundary values are intervals. In addition, we model the right-hand side and coefficient functions as bunches of real functions. Then, we seek the solution of the problem as a bunch of functions. We interpret the IBVP as a set of classical BVPs. Such a classical BVP is constructed by taking a real number from each boundary interval, and a real function from each bunch. We define the bunch consisting of the solutions of all the classical BVPs to be the solution of the IBVP. In this context, we develop a numerical method to obtain the solution. We reduce the complexity of the method from [Formula: see text] to [Formula: see text] through our analysis. We demonstrate the effectiveness of the proposed approach and the numerical method by test examples.

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