摘要
水下爆破荷载作用下各种复合材料、层合结构的力学和工程性状的研究日益引起重视。本文对考虑流固耦合的水下爆破荷载作用下层合板弹性动力响应的计算理论、解析和半解析方法展开研究。
修正了Qing(2007)的数值Laplace逆变换方法在初始点存在的误差,并提出了两种新的逆变换方法,算例表明新方法在不损失精度的情况下降低了计算量,提高了计算效率。
基于Taylor流固耦合理论、Laplace变换和逆变换方法,推导得到了空气中和水下爆破荷载作用下单层Kirchhoff薄板动力响应的级数形式解析解,算例表明：该解析解对薄板具有满意的计算精度。从冲量和能量角度研究了流固耦合效应的作用机理。
建立了一套空气中和水下爆破荷载作用下单层Reissner-Mindlin中厚板动力响应的解析求解流程,与有限元成果的对比验证了该方法的准确性。推导得到了运动方程中分力做功的解析解。算例表明：随着板厚增大,流固耦合效应减弱,板以稀疏波形式向外输出能量的速度减缓。
基于状态空间、精细积分和数值Laplace逆变换方法提出了一套可以考虑流固耦合效应的空气中和水下爆破荷载作用下层合板响应半解析计算方法。单层板算例表明：该方法计算结果更准确,而Kirchhoff板和Mindlin板的误差随厚度增大而增大。层合板算例表明：刚性层和柔性层的分布对板的响应极值有很大影响。
推导得到了指数分布功能梯度层合板冲击(不考虑流固耦合)响应半解析解,在此基础上基于指数层合模型推导得到了任意分布功能梯度层合板冲击(不考虑流固耦合)响应近似解,与均匀层合模型近似解进行对比,验证以上两种方法的准确性。随着分层数目的增加,指数分布层合模型比均匀分布层合模型更快地趋近于精确解。在以上研究的基础上考虑流固耦合,推导得到了空气中和水下爆破荷载作用下功能梯度层合板响应解。
采用线性弹簧层模型模拟弱界面,建立了一套考虑流固耦合效应的爆破荷载作用下功能梯度弱粘结层合板动力响应求解方法。算例表明弱界面对层合板动力响应有较大影响,随着界面柔度系数的增大,弱界面上的位移差也随之增大。
Research on the behavior of composites and laminated structures subjected to underwater explosion load are of great importance. This dissertation investigates the computation theory, analytical and semi-analytical solutions of the elastic dynamic responses of laminated plates subjected to underwater explosion load considering of the fluid-structure-interaction (FSI).
A new algorithm is presented to modify the numerical method (Qing,2007) of the Laplace transform inversion at the initial point. Two new numerical inversion methods of Laplace transform are developed, which reduce the computational complexity without loss of the accuracy.
Based on Taylor's FSI theory, Laplace transform and inversion method, the analytical solution of monolithic Kirchhoff thin plates' response to air or underwater explosion are derived. The results show that the analytical solution based on Kirchhoff plate theory is accurate enough for thin plates. According to the momentum and energy analysis, the FSI mechanism is investigated.
An analytical procedure for solving the elastic dynamic response of the monolithic Ressner-Mindlin plates subjected to air or underwater explosion is proposed. The analytical procedure is verified by comparison with finite element analysis (FEA) results. The analytical solution of the work done by each force component in the motion equations is derived. It is shown that the FSI effect and the energy output efficiency due to the rarefaction wave decrease with the increase of the plate thickness.
Based on state space method. precise integration method and numerical inversion method of Laplace transform a semi-analytical procedure for solving the elastic dynamic response of laminated plates subjected to air or underwater explosion are derived with considering the FSI. Results of monolithic plates show that the semi-analytical procedure is more accurate than FEA method. As the thickness of the plate increases, errors of Kirchhoff and Reissner-Mindlin plate theory increase. Results for laminated plates show that the distributions of the rigid panels and flexible layers in the laminated plates have a great influence on the extreme responses of the laminated plates.
The responses of monolithic functional graded laminated plates subjected to impulsive load (without considering FSI) are investigated. A semi-analytical impulsive response solution for monolithic functional graded plates with exponential law distribution along the thickness coordinate is derived. Based on the semi-analytical impulsive response solution, the exponential layer model (ELM) is used to approximate monolithic functional graded plates with arbitrary distribution along the thickness coordinate, and an approximated solution is derived. The two solutions are verified by comparisons with the approximated results of homogeneous layer model (HLM). It is shown that as the layer counts increase, exponential layer model reach the exact solution faster than homogeneous layer model. Furthermore, based on the solutions for monolithic functional graded laminated plates subjected to impulsive load, and with considering the FSI, the solutions for the responses of laminated functional graded plates subjected to air and underwater explosions loads are derived.
The spring layer model is used to simulate the weak-bonding interface. With considering the FSI, the elastic dynamic response of laminated functional graded plates with weak-bonding interface subjected to air and underwater explosions loads is investigated, and a procedure for solving the response problem is proposed. It is shown that the weak-bonding interface has a relatively great influence on the responses of the laminated plates. As the flexibility of the weak-bonding interface increase, the interface slip also increase.
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