水下爆破荷载作用下简支Kirchhoff板的积分变换解  

On the integral transform method for dynamic response solutions of simply supported Kirchhoff plates with underwater explosion loading

作　　者：王振宇[1] 梁旭[1] 刘国华[1] 程围峰[1] 

机构地区：[1]浙江大学水工结构与水环境研究所,浙江杭州310058

出　　处：《浙江大学学报（工学版）》2011年第11期1972-1979,共8页Journal of Zhejiang University：Engineering Science

基　　金：国家自然科学基金资助项目(50509021;51079127)

摘　　要：为了获得水下爆破荷载下板的动力响应,在空间上采用有限Fourier积分变换,时间上采用Laplace变换,根据Taylor一维流固耦合理论推导得到不考虑流固耦合、气背和液背3种简支薄板的解析解.建立水下爆破荷载下的等边、简支板算例模型,对典型点的Von Mises应力时程、薄板的应力和挠度分布进行比较,解析解与有限元成果吻合良好.对薄板的挠度和应力开展关于弹性模量、板厚的参数分析,并与不考虑弯矩效应的一维解析解对比,研究表明:积分变换解析方法能够给出整个板上的应力和挠度分布,较好地处理流固耦合、边界约束和弯矩效应,更符合实际,也更具有实用价值.In order to get the dynamic response of plates under theunderwater explosion loading,analytical solutions of simply supported Kirchhoff plates were derived by Laplace transform in the time domain and finite Fourier（sine） integral transform in the space domain.The one dimensional Taylor fluid-solid interaction（FSI） was also incorporated.Three boundary conditions,such as plates without considering fluid-solid interaction,air-backed plates and water-backed plates,were soundly studied.An equilateral simply supported model had been established,and comparisons of the Von Mises stress time-histories,the distributions of deflection and Von Mises on the plate between the analytical solutions and FEA results were carried out.The results show that the analytical solutions have a good accuracy.Deflection and Von Mises stress parametric analysis of the elasticity modulus and thickness had been carried out.According to the comparison between the integral transform method and the one dimensional analytical solution without considering bending effect,it is concluded that the integral transform method has more advantage to deal with the fluid-solid interaction,boundary constraint and bending effect.And,the proposed method is more realistic and practical than the one dimensional analytical solution without considering bending effect.

关 键 词：拉普拉斯变换 有限Fourier积分变换 水下爆破 Kirchhoff薄板 冲击动力响应 流固耦合 解析解 

分 类 号：TV542.5[水利工程—水利水电工程] O383[理学—流体力学]