具损伤弹塑性层合结构的非线性力学行为研究
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摘要
本论文以具层内基体损伤以及层间界面损伤的弹塑性层合板为研究对象,综合考虑损伤效应、物理非线性和几何非线性等因素,系统地研究了具损伤弹塑性层合板的屈曲、后屈曲、非线性动力响应,以及压电主动控制等关键力学问题,揭示了该类结构的力学特性及其破坏机制。其研究工作不仅丰富和发展了弹塑性损伤理论,同时,具有重要的工程应用价值。本论文的主要研究内容如下。
关于具层内基体损伤的弹塑性层合结构非线性力学行为的研究,最关键的工作之一是建立其弹塑性损伤本构方程及损伤演化方程。舍弃经典的Hill屈服准则中应力球张量不产生塑性变形的假设,并将其推广应用于各向异性损伤材料,建立了全新的各向异性损伤材料的广义混合硬化屈服准则；在连续介质损伤理论的框架下,基于不可逆热力学原理和广义混合硬化屈服准则,导出了增量型弹塑性损伤本构方程和损伤演化方程。在上述工作的基础上,建立了具基体损伤弹塑性层合板的增量型非线性运动控制方程,综合应用Galerkin法、有限差分法、Newmark-β法及迭代法进行求解；详尽研究了具基体损伤弹塑性层合板的屈曲、后屈曲以及非线性动力响应问题,讨论了损伤效应、荷载参数、几何参数、材料参数等对其非线性静、动力学行为的影响,以及具基体损伤弹塑性层合板与弹性层合板非线性静、动力学行为的差别；同时,采用耦合正、逆压电效应的负速度反馈控制律,通过压电片实现了对具基体损伤弹塑性层合板的主动控制,讨论了反馈控制增益、压电片位置等对控制效果的影响,并比较了对弹塑性层合板与弹性层合板分别实现压电控制后的控制效果。
关于具界面损伤的弹塑性层合结构非线性力学行为的研究,建立了两种各具特色的分析模型。其一是采用界面弱结合本构关系,通过在位移场中引入Heaviside阶跃函数和形函数以反映层间界面损伤,根据Von Karman型非线性板理论,建立了基于弱结合理论的界面损伤分析模型；在上述工作的基础上,推导出具界面损伤弹塑性层合板的增量型压屈平衡方程,运用Galerkin法和迭代法求解,对其屈曲问题进行了分析；详尽讨论了界面损伤、诱导荷载比、材料各向异性等因素对其屈曲临界荷载的影响。其二是通过引入Cohesive Zone的界面损伤预测方法,考虑界面损伤的演化,得到了增量型界面损伤本构方程和损伤演化方程,结合Shear-Lag理论,建立了全新的且形式简洁的弹塑性层合结构界面损伤分析模型。该模型极大简化了界面损伤问题的力学分析,适用于研究考虑界面损伤演化的弹塑性层合结构的非线性静、动力学问题。基于该模型,建立了具界面损伤弹塑性层合板的增量型非线性运动控制方程,采用有限差分法、Newmark-β法和迭代法对整个问题进行求解,详尽讨论了界面损伤对弹塑性层合板中应力与位移分布、非线性时程响应的影响。
In this dissertation, considering elasto-plastic laminated plates with matrix crack damage and interfacial damage, the buckling, postbuckling, nonlinear dynamic response behaviors as well as the piezoelectric active control of elasto-plastic laminated plates with damage are systematically studied, and the essential character of the mechanical property can be illustrated precisely. The research results not only contribute to the enrichment and development of elasto-plastic damage theory, but also have an important meaning in the practical engineering. The main results contain as follows.
The nonlinear mechanical behaviors of elasto-plastic laminated plates with matrix crack damage are investigated. Based on the assumption that the plastic deformation is related to the spherical stress tensor, a new generalized mixed hardening yield criterion for anisotropic damage materials is presented. Then using the continuum damage mechanics theory, and in the basis of the irreversible thermodynamic theory and the generalized mixed hardening yield criterion, the new incremental elasto-plastic damage constitutive equations and damage evolution equations are deduced. By adopting the above constitutive relations, and using the nonlinear plate theory, the incremental nonlinear dynamic governing equations for elasto-plastic laminated plates with matrix crack damage are established. Through applying the Galerkin method, finite difference method, Newmark-βmethod and iterative procedure, the governing equations are solved. The buckling, postbuckling and nonlinear dynamic responses for elasto-plastic laminated plates with matrix crack damage are analyzed. The influences of damage effect, load parameters, geometric and material parameters on the nonlinear static/dynamic behaviors are discussed in detail, and the differences of the mechanical behaviors between the elastic laminated plates and elasto-plastic laminated plates with matrix crack damage are revealed. Meanwhile, a simple negative velocity feed back control algorithm coupling the direct and converse piezoelectric effects is used to actively control the dynamic response of the elasto-plastic plates with matrix crack damage through closed loop control. The influences of feedback control gain and piezoelectric patches's position on the control effect are discussed, and the comparisons of the control effect between the elastic laminated plates and elasto-plastic laminated plates are given.
The nonlinear mechanical behaviors of elasto-plastic laminated plates with interfacial damage are investigated. Two characteristic analysis models are developed. Without considering the interfacial damage evolution, and using the interfacial weakly bonded constitutive relations, a displacement field that reflects the interfacial damage is proposed by introducing the Heaviside step function and shape functions. Then applying the Von Karman nonlinear plate theory, the first interfacial damage analysis model based on the interfacial weakly bonded model is established. On the basis of this model, the incremental buckling equilibrium equation for elasto-plastic laminated plates with interfacial damage is derived. Through applying the Galerkin method and iterative process, the equation is solved. The effects of interfacial damage, induced load ratio and material anisotropy on the critical buckling load of elasto-plastic laminated plates are discussed. The second model is based on the Shear-Lag theory. Considering the interfacial damage evolution, and by using the Cohesive Zone theory, the incremental interfacial damage constitutive equations and damage evolution equations are established. Then by associating with the Shear-Lag theory, a new and simple model for elasto-plastic laminated structures with interfacial damage is established. The model simplifies the interfacial damage problems greatly, and suits for the nonlinear mechanical analysis of both elastic and elasto-plastic laminated structures. On the basis of the model, the incremental nonlinear dynamic governing equations are obtained, and the difference method, Newmark-βmethod and iterative procedure are adopted to solve the equations. The effects of interfacial damage on stress and displacement distributions, nonlinear dynamic response of elasto-plastic laminated plates are discussed in detail.
关于具层内基体损伤的弹塑性层合结构非线性力学行为的研究,最关键的工作之一是建立其弹塑性损伤本构方程及损伤演化方程。舍弃经典的Hill屈服准则中应力球张量不产生塑性变形的假设,并将其推广应用于各向异性损伤材料,建立了全新的各向异性损伤材料的广义混合硬化屈服准则；在连续介质损伤理论的框架下,基于不可逆热力学原理和广义混合硬化屈服准则,导出了增量型弹塑性损伤本构方程和损伤演化方程。在上述工作的基础上,建立了具基体损伤弹塑性层合板的增量型非线性运动控制方程,综合应用Galerkin法、有限差分法、Newmark-β法及迭代法进行求解；详尽研究了具基体损伤弹塑性层合板的屈曲、后屈曲以及非线性动力响应问题,讨论了损伤效应、荷载参数、几何参数、材料参数等对其非线性静、动力学行为的影响,以及具基体损伤弹塑性层合板与弹性层合板非线性静、动力学行为的差别；同时,采用耦合正、逆压电效应的负速度反馈控制律,通过压电片实现了对具基体损伤弹塑性层合板的主动控制,讨论了反馈控制增益、压电片位置等对控制效果的影响,并比较了对弹塑性层合板与弹性层合板分别实现压电控制后的控制效果。
关于具界面损伤的弹塑性层合结构非线性力学行为的研究,建立了两种各具特色的分析模型。其一是采用界面弱结合本构关系,通过在位移场中引入Heaviside阶跃函数和形函数以反映层间界面损伤,根据Von Karman型非线性板理论,建立了基于弱结合理论的界面损伤分析模型；在上述工作的基础上,推导出具界面损伤弹塑性层合板的增量型压屈平衡方程,运用Galerkin法和迭代法求解,对其屈曲问题进行了分析；详尽讨论了界面损伤、诱导荷载比、材料各向异性等因素对其屈曲临界荷载的影响。其二是通过引入Cohesive Zone的界面损伤预测方法,考虑界面损伤的演化,得到了增量型界面损伤本构方程和损伤演化方程,结合Shear-Lag理论,建立了全新的且形式简洁的弹塑性层合结构界面损伤分析模型。该模型极大简化了界面损伤问题的力学分析,适用于研究考虑界面损伤演化的弹塑性层合结构的非线性静、动力学问题。基于该模型,建立了具界面损伤弹塑性层合板的增量型非线性运动控制方程,采用有限差分法、Newmark-β法和迭代法对整个问题进行求解,详尽讨论了界面损伤对弹塑性层合板中应力与位移分布、非线性时程响应的影响。
In this dissertation, considering elasto-plastic laminated plates with matrix crack damage and interfacial damage, the buckling, postbuckling, nonlinear dynamic response behaviors as well as the piezoelectric active control of elasto-plastic laminated plates with damage are systematically studied, and the essential character of the mechanical property can be illustrated precisely. The research results not only contribute to the enrichment and development of elasto-plastic damage theory, but also have an important meaning in the practical engineering. The main results contain as follows.
The nonlinear mechanical behaviors of elasto-plastic laminated plates with matrix crack damage are investigated. Based on the assumption that the plastic deformation is related to the spherical stress tensor, a new generalized mixed hardening yield criterion for anisotropic damage materials is presented. Then using the continuum damage mechanics theory, and in the basis of the irreversible thermodynamic theory and the generalized mixed hardening yield criterion, the new incremental elasto-plastic damage constitutive equations and damage evolution equations are deduced. By adopting the above constitutive relations, and using the nonlinear plate theory, the incremental nonlinear dynamic governing equations for elasto-plastic laminated plates with matrix crack damage are established. Through applying the Galerkin method, finite difference method, Newmark-βmethod and iterative procedure, the governing equations are solved. The buckling, postbuckling and nonlinear dynamic responses for elasto-plastic laminated plates with matrix crack damage are analyzed. The influences of damage effect, load parameters, geometric and material parameters on the nonlinear static/dynamic behaviors are discussed in detail, and the differences of the mechanical behaviors between the elastic laminated plates and elasto-plastic laminated plates with matrix crack damage are revealed. Meanwhile, a simple negative velocity feed back control algorithm coupling the direct and converse piezoelectric effects is used to actively control the dynamic response of the elasto-plastic plates with matrix crack damage through closed loop control. The influences of feedback control gain and piezoelectric patches's position on the control effect are discussed, and the comparisons of the control effect between the elastic laminated plates and elasto-plastic laminated plates are given.
The nonlinear mechanical behaviors of elasto-plastic laminated plates with interfacial damage are investigated. Two characteristic analysis models are developed. Without considering the interfacial damage evolution, and using the interfacial weakly bonded constitutive relations, a displacement field that reflects the interfacial damage is proposed by introducing the Heaviside step function and shape functions. Then applying the Von Karman nonlinear plate theory, the first interfacial damage analysis model based on the interfacial weakly bonded model is established. On the basis of this model, the incremental buckling equilibrium equation for elasto-plastic laminated plates with interfacial damage is derived. Through applying the Galerkin method and iterative process, the equation is solved. The effects of interfacial damage, induced load ratio and material anisotropy on the critical buckling load of elasto-plastic laminated plates are discussed. The second model is based on the Shear-Lag theory. Considering the interfacial damage evolution, and by using the Cohesive Zone theory, the incremental interfacial damage constitutive equations and damage evolution equations are established. Then by associating with the Shear-Lag theory, a new and simple model for elasto-plastic laminated structures with interfacial damage is established. The model simplifies the interfacial damage problems greatly, and suits for the nonlinear mechanical analysis of both elastic and elasto-plastic laminated structures. On the basis of the model, the incremental nonlinear dynamic governing equations are obtained, and the difference method, Newmark-βmethod and iterative procedure are adopted to solve the equations. The effects of interfacial damage on stress and displacement distributions, nonlinear dynamic response of elasto-plastic laminated plates are discussed in detail.
引文
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