基于损伤理论的预应力混凝土梁弹性模量分析
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摘要
针对混凝土材料在成型过程中不可避免的存在微裂缝和微孔隙的特点,定义了基于混凝土弹性模量表达的负损伤变量,把负损伤变量引入到损伤本构方程中,采用损伤力学附加荷载有限元法对体外预应力混凝土梁的受力过程进行了分析,得到了预应力混凝土梁的弹性模量随预应力变化的规律。结果表明:引入负损伤变量可以很好地模拟混凝土弹性模量的变化,特别是施加预应力阶段;运用求得的混凝土弹性模量对某试验梁的自振频率进行分析,计算结果在变化趋势上是和试验结果相一致,并且误差在可以接受的范围之内。
It's not avoidable of the concrete material to produce micro-fractures and micro-hole at the shaping process.In the light of this feature,the author defines a negative damage variable based on the concrete elastic modulus,and introduces the negative damage variable to the damage constitutive equation.The relation between the elastic modulus of the prestressed concrete beam with various prestressing force is obtained by analyzing the dynamic behaviors of the externally prestressed concrete structures using the damage mechanics and load finite-element method.The results indicate: the damage theory with the negative damage variation based on the concrete elastic modulus can predict well the variation of the concrete elastic modulus,especially at the stage in application of pre-stress;the natural frequency determined by the elastic modulus in the corresponding state is consistent with the test results in trend,and the error is acceptable.
It's not avoidable of the concrete material to produce micro-fractures and micro-hole at the shaping process.In the light of this feature,the author defines a negative damage variable based on the concrete elastic modulus,and introduces the negative damage variable to the damage constitutive equation.The relation between the elastic modulus of the prestressed concrete beam with various prestressing force is obtained by analyzing the dynamic behaviors of the externally prestressed concrete structures using the damage mechanics and load finite-element method.The results indicate: the damage theory with the negative damage variation based on the concrete elastic modulus can predict well the variation of the concrete elastic modulus,especially at the stage in application of pre-stress;the natural frequency determined by the elastic modulus in the corresponding state is consistent with the test results in trend,and the error is acceptable.
引文
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[2]张耀庭,汪霞利,李瑞鸽.全预应力梁振动频率的理论分析与试验研究[J].工程力学,2007,24(8):116―120.Zhang Yaoting,Wang Xiali,Li Ruige.Experimental and theoretical research on vibration frequency of full-prestressed concrete beam[J].Engineering Mechanics,2007,24(8):116―120.(in Chinese)
[3]Saiidi M,Douglas B,Feng S.Prestress force effect on vibration frequency of concrete bridges[J].Journal of structural Engineering,1994,120(7):2233―2241.
[4]Tang X S,Jiang C P,Zheng J L.General expressions of constitutive equations for isotropic elastic damaged materials[J].Applied Mathematics and Mechanics(English Edition),2001,22(12):1468―1475.
[5]尹双增.断裂损伤理论及应用[M].北京:清华大学出版社,1992.Yin Shuangzeng.Fracture damage mechanics and application[M].Beijing:Tsinghua University Press,1992.(in Chinese)
[6]Tang X S,Jiang C P,Zheng J L.Anisotropic elastic constitutive relations for damaged materials by application of irreversible thermodynamics[J].Theoretical and Applied Fracture Mechanics,2002,38(3):211―220.
[7]Tang X S,Zhang J R,Li C X.Damage analysis and numerical simulation for failure process of a reinforced concretearch structure[J].Computers and Structures,2005,83(31-32):2609―2631.
[8]Xiong Huixia,Zhang Yaoting.Experimental and theoretical analysis on the natural frequency of external prestressed concrete beams[J].Journal of Chongqing University(English Edition),2008,7(4):317―323.
[9]李宏健.无粘结全预应力砼简支梁动力性能研究[D].武汉:华中科技大学,2007.Li Hongjian.Experimental study on dynamic behavior of full-prestressed concrete beams[D].Wuhan:Huazhong University of Science&Technology,2007.(in Chinese)
[10]熊学玉,王寿生.体外预应力梁振动特性的分析与研究[J].地震工程与工程振动,2005,25(2):55―61.Xiong Xueyu,Wang Shousheng.Analysis and research of externally prestressed concrete beam vibration behavior[J].Earthquake Engineering and Engineering Vibration,2005,25(2):55―61.(in Chinese)
[2]张耀庭,汪霞利,李瑞鸽.全预应力梁振动频率的理论分析与试验研究[J].工程力学,2007,24(8):116―120.Zhang Yaoting,Wang Xiali,Li Ruige.Experimental and theoretical research on vibration frequency of full-prestressed concrete beam[J].Engineering Mechanics,2007,24(8):116―120.(in Chinese)
[3]Saiidi M,Douglas B,Feng S.Prestress force effect on vibration frequency of concrete bridges[J].Journal of structural Engineering,1994,120(7):2233―2241.
[4]Tang X S,Jiang C P,Zheng J L.General expressions of constitutive equations for isotropic elastic damaged materials[J].Applied Mathematics and Mechanics(English Edition),2001,22(12):1468―1475.
[5]尹双增.断裂损伤理论及应用[M].北京:清华大学出版社,1992.Yin Shuangzeng.Fracture damage mechanics and application[M].Beijing:Tsinghua University Press,1992.(in Chinese)
[6]Tang X S,Jiang C P,Zheng J L.Anisotropic elastic constitutive relations for damaged materials by application of irreversible thermodynamics[J].Theoretical and Applied Fracture Mechanics,2002,38(3):211―220.
[7]Tang X S,Zhang J R,Li C X.Damage analysis and numerical simulation for failure process of a reinforced concretearch structure[J].Computers and Structures,2005,83(31-32):2609―2631.
[8]Xiong Huixia,Zhang Yaoting.Experimental and theoretical analysis on the natural frequency of external prestressed concrete beams[J].Journal of Chongqing University(English Edition),2008,7(4):317―323.
[9]李宏健.无粘结全预应力砼简支梁动力性能研究[D].武汉:华中科技大学,2007.Li Hongjian.Experimental study on dynamic behavior of full-prestressed concrete beams[D].Wuhan:Huazhong University of Science&Technology,2007.(in Chinese)
[10]熊学玉,王寿生.体外预应力梁振动特性的分析与研究[J].地震工程与工程振动,2005,25(2):55―61.Xiong Xueyu,Wang Shousheng.Analysis and research of externally prestressed concrete beam vibration behavior[J].Earthquake Engineering and Engineering Vibration,2005,25(2):55―61.(in Chinese)
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