Aiming at the circular chamber under uniform stress field in deep energy storage and mining,analytical solutions of stress and plastic zone of the surrounding rock under different far-field stress and internal pressur...Aiming at the circular chamber under uniform stress field in deep energy storage and mining,analytical solutions of stress and plastic zone of the surrounding rock under different far-field stress and internal pressure were derived based on bi-modulus theory and the elastic-brittle-ideal plastic constitutive model.Evolution trend of the elasticplastic stress and plastic region with different elastic constant ratios and residual strength coefficients were analyzed in details.Results revealed that when the internal pressure was small,the three-direction principal stress was compressive stress and the stress field distribution of the surrounding rock was not affected by the moduli difference.The obtained solution was consistent with the solution from the elastic-brittle plastic drop model under the equal modulus theory.On the other hand,when the internal pressure was large,the tangential stress was changed.The surrounding rock can be divided into three zones,i.e.,tensile plastic zone(TPZ),tensile elastic zone(TEZ)and compressive elastic zone(CEZ).The tensile and compressive dual modulus had significant influence on the demarcation point between TEZ and CEZ.In addition,the strength drop and the dual modulus characteristic had a coupling effect on the stress distribution in the surrounding rock.The related achievements further enrich the theory of deep rock mechanics.展开更多
A unified stress function for bi-modulus beams is proposed based on its mechanic sense on the boundary of beams. Elasticity solutions of stress and displacement for bi-modulus beams under combined loads are derived. T...A unified stress function for bi-modulus beams is proposed based on its mechanic sense on the boundary of beams. Elasticity solutions of stress and displacement for bi-modulus beams under combined loads are derived. The example analysis shows that the maximum tensile stress using the same elastic modulus theory is underestimated if the tensile elastic modulus is larger than the compressive elastic modulus. Otherwise, the maximum compressive stress is underestimated. The maximum tensile stress using the material mechanics solution is underestimated when the tensile elastic modulus is larger than the compressive elastic modulus to a certain extent. The error of stress using the material mechanics theory decreases as the span-to-height ratio of beams increases, which is apparent when L/h ≤ 5. The error also varies with the distributed load patterns.展开更多
The materials with different moduli in tension and compression are called bi-modulus materials. Graphene is such a kind of materials with the highest strength and the thinnest thickness. In this paper, the mechanical ...The materials with different moduli in tension and compression are called bi-modulus materials. Graphene is such a kind of materials with the highest strength and the thinnest thickness. In this paper, the mechanical response of the bi-modulus beam subjected to the temperature effect and placed on the Winkler foundation is studied. The differential equations about the neutral axis position and undetermined parameters of the normal strain of the bi-modulus foundation beam are established. Then, the analytical expressions of the normal stress, bending moment, and displacement of the foundation beam are derived. Simultaneously, a calculation procedure based on the finite element method （FEM） is developed to obtain the temperature stress of the bi-modulus struc- tures. It is shown that the obtained bi-modulus solutions can recover the classical modulus solution, and the results obtained by the analytical expressions, the present FEM proce- dure, and the traditional FEM software are consistent, which verifies the accuracy and reliability of the present analytical model and procedure. Finally, the difference between the bi-modulus results and the classical same modulus results is discussed, and several reasonable suggestions for calculating and optimizing the certain bi-modulus member in practical engineering are presented.展开更多
In nature,there are widely distributed bi-modulus materials with different deformation characteristics under compressive and tensile stress states,such as concrete,rock and ceramics.Due to the lack of constitutive mod...In nature,there are widely distributed bi-modulus materials with different deformation characteristics under compressive and tensile stress states,such as concrete,rock and ceramics.Due to the lack of constitutive model that could reasonably consider the bi-modulus property of materials,and the lack of simple and reliable measurement methods for the tensile elastic parameters of materials,scientists and engineers always neglect the effect of the bi-modulus property of materials in engineering design and numerical simulation.To solve this problem,this study utilizes the uncoupled strain-driven constitutive model proposed by Latorre and Montáns(2020)to systematically study the distributions and magnitudes of stresses and strains of bi-modulus materials in the three-point bending test through the numerical method.Furthermore,a new method to synchronously measure the tensile and compressive elastic moduli of materials through the four-point bending test is proposed.The numerical results show that the bi-modulus property of materials has a significant effect on the stress,strain and displacement in the specimen utilized in the three-point and four-point bending tests.Meanwhile,the results from the numerical tests,in which the elastic constitutive model proposed by Latorre and Montáns(2020)is utilized,also indicate that the newly proposed measurement method has a good reliability.Although the new measurement method proposed in this study can synchronously and effectively measure the tensile and compressive elastic moduli,it cannot measure the tensile and compressive Poisson’s ratios.展开更多
By taking into account the effect of the bi-modulus for tension and compression of the fiber reinforced polymer （FRP） sheet in the reinforcement layer, a general mathematical model for the nonlinear bending of a sle...By taking into account the effect of the bi-modulus for tension and compression of the fiber reinforced polymer （FRP） sheet in the reinforcement layer, a general mathematical model for the nonlinear bending of a slender timber beam strengthened with the FRP sheet is established under the hypothesis of the large deflection deformation of the beam. Nonlinear governing equations of the second order effect of the beam bending are derived. The nonlinear stability of a simply-supported slender timber column strengthened with the FRP sheet is then investigated. An expression of the critical load of the simply-supported FRP-strengthened timber beam is obtained. The existence of postbuckling solution of the timber column is proved theoretically, and an asymptotic analytical solution of the postbuckling state in the vicinity of the critical load is obtained using the perturbation method. Parameters are studied showing that the FRP reinforcement layer has great influence on the critical load of the timber column, and has little influence on the dimensionless postbuckling state.展开更多
基金Projects(51774196,52074169)supported by the National Natural Science Foundation of China。
文摘Aiming at the circular chamber under uniform stress field in deep energy storage and mining,analytical solutions of stress and plastic zone of the surrounding rock under different far-field stress and internal pressure were derived based on bi-modulus theory and the elastic-brittle-ideal plastic constitutive model.Evolution trend of the elasticplastic stress and plastic region with different elastic constant ratios and residual strength coefficients were analyzed in details.Results revealed that when the internal pressure was small,the three-direction principal stress was compressive stress and the stress field distribution of the surrounding rock was not affected by the moduli difference.The obtained solution was consistent with the solution from the elastic-brittle plastic drop model under the equal modulus theory.On the other hand,when the internal pressure was large,the tangential stress was changed.The surrounding rock can be divided into three zones,i.e.,tensile plastic zone(TPZ),tensile elastic zone(TEZ)and compressive elastic zone(CEZ).The tensile and compressive dual modulus had significant influence on the demarcation point between TEZ and CEZ.In addition,the strength drop and the dual modulus characteristic had a coupling effect on the stress distribution in the surrounding rock.The related achievements further enrich the theory of deep rock mechanics.
基金Project supported by the Doctoral Fund of Ministry of Education of China(No.20103108110019)the National Natural Science Foundation of China(No.51208292)the National Key Technology R&D Programs(Nos.2011BAG07B01 and 2012BAK24B04)
文摘A unified stress function for bi-modulus beams is proposed based on its mechanic sense on the boundary of beams. Elasticity solutions of stress and displacement for bi-modulus beams under combined loads are derived. The example analysis shows that the maximum tensile stress using the same elastic modulus theory is underestimated if the tensile elastic modulus is larger than the compressive elastic modulus. Otherwise, the maximum compressive stress is underestimated. The maximum tensile stress using the material mechanics solution is underestimated when the tensile elastic modulus is larger than the compressive elastic modulus to a certain extent. The error of stress using the material mechanics theory decreases as the span-to-height ratio of beams increases, which is apparent when L/h ≤ 5. The error also varies with the distributed load patterns.
基金supported by the National Natural Science Foundation of China(Nos.11072143 and11272200)
文摘The materials with different moduli in tension and compression are called bi-modulus materials. Graphene is such a kind of materials with the highest strength and the thinnest thickness. In this paper, the mechanical response of the bi-modulus beam subjected to the temperature effect and placed on the Winkler foundation is studied. The differential equations about the neutral axis position and undetermined parameters of the normal strain of the bi-modulus foundation beam are established. Then, the analytical expressions of the normal stress, bending moment, and displacement of the foundation beam are derived. Simultaneously, a calculation procedure based on the finite element method （FEM） is developed to obtain the temperature stress of the bi-modulus struc- tures. It is shown that the obtained bi-modulus solutions can recover the classical modulus solution, and the results obtained by the analytical expressions, the present FEM proce- dure, and the traditional FEM software are consistent, which verifies the accuracy and reliability of the present analytical model and procedure. Finally, the difference between the bi-modulus results and the classical same modulus results is discussed, and several reasonable suggestions for calculating and optimizing the certain bi-modulus member in practical engineering are presented.
基金funding support from the National Key Research and Development Program of China(Grant No.2022YFC3102402)as well as from the National Natural Science Foundation of China(Grant No.51879257).
文摘In nature,there are widely distributed bi-modulus materials with different deformation characteristics under compressive and tensile stress states,such as concrete,rock and ceramics.Due to the lack of constitutive model that could reasonably consider the bi-modulus property of materials,and the lack of simple and reliable measurement methods for the tensile elastic parameters of materials,scientists and engineers always neglect the effect of the bi-modulus property of materials in engineering design and numerical simulation.To solve this problem,this study utilizes the uncoupled strain-driven constitutive model proposed by Latorre and Montáns(2020)to systematically study the distributions and magnitudes of stresses and strains of bi-modulus materials in the three-point bending test through the numerical method.Furthermore,a new method to synchronously measure the tensile and compressive elastic moduli of materials through the four-point bending test is proposed.The numerical results show that the bi-modulus property of materials has a significant effect on the stress,strain and displacement in the specimen utilized in the three-point and four-point bending tests.Meanwhile,the results from the numerical tests,in which the elastic constitutive model proposed by Latorre and Montáns(2020)is utilized,also indicate that the newly proposed measurement method has a good reliability.Although the new measurement method proposed in this study can synchronously and effectively measure the tensile and compressive elastic moduli,it cannot measure the tensile and compressive Poisson’s ratios.
基金Project supported by the National High Technology Research and Development Program(No. 2009AA032303-2)
文摘By taking into account the effect of the bi-modulus for tension and compression of the fiber reinforced polymer （FRP） sheet in the reinforcement layer, a general mathematical model for the nonlinear bending of a slender timber beam strengthened with the FRP sheet is established under the hypothesis of the large deflection deformation of the beam. Nonlinear governing equations of the second order effect of the beam bending are derived. The nonlinear stability of a simply-supported slender timber column strengthened with the FRP sheet is then investigated. An expression of the critical load of the simply-supported FRP-strengthened timber beam is obtained. The existence of postbuckling solution of the timber column is proved theoretically, and an asymptotic analytical solution of the postbuckling state in the vicinity of the critical load is obtained using the perturbation method. Parameters are studied showing that the FRP reinforcement layer has great influence on the critical load of the timber column, and has little influence on the dimensionless postbuckling state.
