The relation between invariant integrals of the linear isotropic theory of elasticity and integrals defined by the duality principle

2009 ◽  
Vol 73 (2) ◽  
pp. 237-243 ◽  
Author(s):  
Ye.I. Shifrin
2020 ◽  
Vol 26 (1) ◽  
pp. 80-89
Author(s):  
AN Soloviev ◽  
BV Sobol ◽  
EV Rashidova ◽  
AI Novikova

We analysed the problem of determining the exponents in the asymptotic solution of the isotropic theory of elasticity problem at the top of the wedge-shaped region where its sides (or one of them) are supported by a thin coating and lean without friction on the rigid bases. On the other side of the wedge-shaped region, it is assumed that there are various boundary conditions, including when there is a thin coating. Mathematically, the problem reduces to the problem of determining the roots of transcendental characteristic equations arising from the condition for the existence of a nontrivial solution of a system of the linear homogeneous equations. The characteristics of the stress tensor components have been determined for the various combinations of boundary conditions and physical and geometric parameters. The qualitative conclusions are made. In particular, we have established the combinations of the values of these parameters at which the singular behaviour of stresses arises.


Author(s):  
Chunyu Liu ◽  
Fengrui Mu ◽  
Weilong Zhang

Background: In recent era of technology, the traditional Ant Colony Algorithm (ACO) is insufficient in solving the problem of network congestion and load balance, and network utilization. Methods: This paper proposes an improved ant colony algorithm, which considers the price factor based on the theory of elasticity of demand. The price factor is denominated in the impact on the network load which means indirect control of network load, congestion or auxiliary solution to calculate the idle resources caused by the low network utilization and reduced profits. Results: Experimental results show that the improved algorithm can balance the overall network load, extend the life of path by nearly 3 hours, greatly reduce the risk of network paralysis, and increase the profit of the manufacturer by 300 million Yuan. Conclusion: Furthermore, results shows that the improved method has a great application value in improving the network efficiency, balancing network load, prolonging network life and increasing network operating profit.


2008 ◽  
Vol 43 (3) ◽  
pp. 437-452 ◽  
Author(s):  
A. V. Kaptsov ◽  
E. I. Shifrin

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