悬臂梁在冲击荷载作用下的弹塑性响应分析
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摘要
针对悬臂梁在冲击荷载作用下的弹塑性动力响应进行研究,利用有限元软件ABAQUS建立悬臂梁模型进行数值分析。对悬臂梁中点施加冲击荷载,通过对响应不同时刻弯矩分布特征的分析,阐明了悬臂梁的弹塑性动力响应模式。结果表明冲击荷载作用下悬臂梁整个响应过程可划分为5个阶段,即弹塑性波对称传播阶段、弹塑性波反射迭加阶段、双驻定铰阶段、根部单铰阶段、弹性自由振动阶段。合理解释了撞击发生后,悬臂梁局部区段所发生的反向弯曲变形,弹塑性分析证实了响应早期弹塑性波反射迭加阶段和双驻定铰阶段的存在性,肯定了刚塑性分析所假定模式的主要特征,从而为发展全面的弹塑性分析模型提供参考。
In order to study the elastic-plastic dynamic response of cantilever beam under impact load, a cantilever beam model was established by using the finite element software ABAQUS for numerical analysis. The impact load on midpoint of cantilever beam was analyzed, and the elastic-plastic dynamic response mode of cantilever beam was clarified by analyzing the distribution characteristics of bending moment at different moments. The results showed that the whole response process of the cantilever beam under the impact load could be divided into five stages, that is, elastic plastic bending wave symmetry propagation stage; elastic-plastic bending wave reflection superposition stage;double stationary hinge stage; root single hinge stage;elastic free vibration stage. The reverse bending deformation occurred in the local section of the cantilever beam after the impact was explained, and the elastic-plastic analysis confirmed the existence of the elastic-plastic bending wave reflection stage and the double stationary hinge stage in the early response, and confirmed the main characteristics of the assumed model of the rigid plastic analysis, so as to develop the comprehensive elastic-plastic analysis. The analysis model could provide better guidance.
In order to study the elastic-plastic dynamic response of cantilever beam under impact load, a cantilever beam model was established by using the finite element software ABAQUS for numerical analysis. The impact load on midpoint of cantilever beam was analyzed, and the elastic-plastic dynamic response mode of cantilever beam was clarified by analyzing the distribution characteristics of bending moment at different moments. The results showed that the whole response process of the cantilever beam under the impact load could be divided into five stages, that is, elastic plastic bending wave symmetry propagation stage; elastic-plastic bending wave reflection superposition stage;double stationary hinge stage; root single hinge stage;elastic free vibration stage. The reverse bending deformation occurred in the local section of the cantilever beam after the impact was explained, and the elastic-plastic analysis confirmed the existence of the elastic-plastic bending wave reflection stage and the double stationary hinge stage in the early response, and confirmed the main characteristics of the assumed model of the rigid plastic analysis, so as to develop the comprehensive elastic-plastic analysis. The analysis model could provide better guidance.
引文
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[7] YU T X, YANG J L, REID S R. Interaction Between Reflected Elastic Flexural Waves and a Plastic ‘Hinge’ in the Dynamic Response of Pulse Loaded Beams[J]. Impact Engng, 1997, 19(5/6):457-475.
[8] 周青, 余同希.强动载荷作用下变截面梁中的塑性铰[J].爆炸与冲击, 1987, 7(4):311-318.
[9] SYMONDS P S. Survey of Methods of Analysis for Plastic Deformation of Structure Under Dynamic Loading[R].Division of Engineering Report. Rhode Island: Brown University, 1967.
[10]ZHANG T G, STRONGE W J, YU T X. Dynamic Deformation of Rigid-Plastic Beam for General Impulsive Loading:a Phenomenological Mode[J]. Impact Engng, 1995, 16(4):535-562.
[11]STRONG W J, YU T X. Dynamic Models for Structural Plasticity[M].London: Springer-Verlag London Limited, 1995.
[12]YU J L,JONES N. Numerical Simulation of a Clamped Beam Under Impact Loading[J].Computer & Structures, 1989,32(2):281-293.
[13]虞吉林, 黄锐.冲击载荷下软钢梁早期响应的数值模拟和简化模型[J]. 力学学报, 1997, 29(4):464-469.
[14]SYMONDS P S, YU T X. Counterintuitive Behavior in a Problem of Elastic-Plastic Beam Dynamics[J].Journal of Applied Mechanics, 1985, 52(4):517-522.
[15]XI F, YANG J L, LI Z L.Anomalous Behavior Revisited:Dynamic Response of Elastic-Plastic Structures[J].Acta Mechanica Solida Sinica, 1998, 11(4):283-294.
[16]HASHMI S J, AL-HASSANI S T S, JOHNSON W. Large Deflection Elastic-Plastic Response of Certain Structures to Impulsive Loads: Numerical Solution and Experimental Results[J].International Journal of Mechanical Science, 1972,14(12):843-860.
[2] 包恩和,王天成,孙凌云,等.不同中部连接的多层钢框架连体结构动力响应研究[J].钢结构,2017,32(3):1-6.
[3] SYMONDS P S, YU T X. Counterintuitive Behavior in a Problem of Elastic-Plastic Beam Dynamics[J]. Journal of Applied Mechanics, 1985, 52:517-522.
[4] 臧晓琳,吕丞丞,董立畅,等.支撑对装配式钢框架抗连续倒塌性能影响[J].钢结构,2018,33(3):16-20.
[5] REID S R, GUI X G. On the Elastic-Plastic Deformation of Cantilever Beams Subjected to Tip Impact[J]. Impact Engng, 1987, 6(2):109-127.
[6] YU J L, JONES N. Numerical Simulation of a Clamped Beam Under Impact Loading[J].Computer & Structures, 1989,32(2):281-293.
[7] YU T X, YANG J L, REID S R. Interaction Between Reflected Elastic Flexural Waves and a Plastic ‘Hinge’ in the Dynamic Response of Pulse Loaded Beams[J]. Impact Engng, 1997, 19(5/6):457-475.
[8] 周青, 余同希.强动载荷作用下变截面梁中的塑性铰[J].爆炸与冲击, 1987, 7(4):311-318.
[9] SYMONDS P S. Survey of Methods of Analysis for Plastic Deformation of Structure Under Dynamic Loading[R].Division of Engineering Report. Rhode Island: Brown University, 1967.
[10]ZHANG T G, STRONGE W J, YU T X. Dynamic Deformation of Rigid-Plastic Beam for General Impulsive Loading:a Phenomenological Mode[J]. Impact Engng, 1995, 16(4):535-562.
[11]STRONG W J, YU T X. Dynamic Models for Structural Plasticity[M].London: Springer-Verlag London Limited, 1995.
[12]YU J L,JONES N. Numerical Simulation of a Clamped Beam Under Impact Loading[J].Computer & Structures, 1989,32(2):281-293.
[13]虞吉林, 黄锐.冲击载荷下软钢梁早期响应的数值模拟和简化模型[J]. 力学学报, 1997, 29(4):464-469.
[14]SYMONDS P S, YU T X. Counterintuitive Behavior in a Problem of Elastic-Plastic Beam Dynamics[J].Journal of Applied Mechanics, 1985, 52(4):517-522.
[15]XI F, YANG J L, LI Z L.Anomalous Behavior Revisited:Dynamic Response of Elastic-Plastic Structures[J].Acta Mechanica Solida Sinica, 1998, 11(4):283-294.
[16]HASHMI S J, AL-HASSANI S T S, JOHNSON W. Large Deflection Elastic-Plastic Response of Certain Structures to Impulsive Loads: Numerical Solution and Experimental Results[J].International Journal of Mechanical Science, 1972,14(12):843-860.