ANALYSIS OF BENDING, VIBRATION AND STABILITY FOR THIN PLATE ON ELASTIC FOUNDATION BY THE MULTIVARIABLE SPLINE ELEMENT METHOD

In this paper, the bicubic splines in product form are used to construct the multi-field functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable spline element equations are derived, based on the mixed variational principle. The analysis and calculations of bending, vibration and stability of the plates on elastic foundation are presented in the paper. Because the field functions of plate on elastic foundation are assumed independently, the precision of the field variables of bending moments and displacement is high.

A FREE RECTANGULAR PLATE ON ELASTIC FOUNDATION

In the theory of elastic thin plates, the bending of a rectangular plate on the elastic foundation is also a difficult problem. This paper provides a rigorous solution by the method of superposition. It satisfies the differential eguation, the boundary conditions of the edges and the free corners. Thus we are led to a system of infinite simultaneous eguations. The problem solved is for a plate with a concentrated load at its center. The reactive forces from the foundation should be made to be in equilibrium with the concentrated force to see whether our calculation is correct or not.

Synergistic instability of coal pillar and roof system and filling method based on plate model

The security challenges from room and pillar gobs include land subsidence, spontaneous combustion of coal pillars and mine flood caused by gob water. To explore the instability mechanism of room and pillar gob, we established a mechanical model of elastic plate on elastic foundation in which pillars and hard roofs were considered as continuous Winkler foundations and elastic plates, respectively. The synergetic instability of pillar and roof system was analyzed based on plate bending theory and catastrophe theory. In addition, mechanical conditions and math criterion of roof failure and overall instability of coal pillar and roof system were given. Through analyzing both advantages and disadvantages of some technologies such as induced caving, filling, gob sealing and isolation, we presented a new filling method named box-filling, in view of box foundation theory, to control the disasters of ground collapse, water inrush and mine fire. In a gob's treatment project in Ordos, safety assessment and filling design of a room and pillar gob have been done by the mechanical model. The results show that the gob will collapse when the pillars' average yield band is wider than 0.93 m, and box-filling can control land collapse, mine flood and mine fire economically and efficiently. So it is worth to study further and popularize.

Influence of backfilling rate on the stability of the"backfilling bodyimmediate roof"cooperative bearing structure

To reduce the cost of backfilling coal mining and utilize the underground space of coal mines,a new backfilling mining method with low backfilling rate called constructional backfilling coal mining(CBCM)is proposed.The "backfilling body-immediate roof" cooperative bearing structure of CBCM is analyzed by establishing the model of the medium thick plate on an elastic foundation.The influence of the backfilling rate on the stability of overlying strata is analyzed by the numerical simulation experiment.The control effect of CBCM is verified by a physic similar simulation test.The economic benefit of CBCM is analyzed.The conclusions are:the deformation characteristics of the immediate roof and critical backfilling spacing in CBCM can be analyzed based on the Hu Haichang’s theory.Exerting the bearing capacity of the immediate roof is beneficial to the stability of the overlying strata.The CBCM has a good control effect on the overburden in Xinyang Mine when the backfilling rate is lower than 25%.The backfilling cost of per ton coal is 37.39 yuan/t when the backfilling rate is 13.7%,with a decrease rate of 56.63%than the full-filling.The research results can provide theoretical support for the application of CBCM in coal mining.