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...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.展开更多
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 ...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.展开更多
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.Th...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.展开更多
文摘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.
文摘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.
基金supported by the Youth Funds of National Natural Science Foundation of China(No.52004173)the Distinguished Youth Funds of National Natural Science Foundation of China(No.51925402)+2 种基金the Science and Technology Innovation Project of Colleges and Universities in Shanxi Province(No.2020L0066)the China Postdoctoral Science Foundation(No.2022M712922)the Shanxi-Zheda Institute of Advanced Materials and Chemical Engineering(Nos.2021SX-TD001 and 2022SXTD008).
文摘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.
