层合板结构振动分析的无网格方法

发布时间：2018-07-06 14:42

本文选题：层合板 + 振动　；参考：《苏州大学》2015年硕士论文

【摘要】：由复合材料铺设而成的层合板具有重量轻、强度高、介电性好、抗腐蚀等性质而被广泛应用于各种工程结构中,如飞机的机翼、高铁的车厢、汽车的胎面以及人造卫星的太阳风帆等。随着使用环境对材料的要求越发苛刻,层合板的振动问题也越来越被重视。因此,对层合板的振动研究具有重要的工程意义。各阶频率、动态响应及模态是层合板振动数值计算中最基本的三个问题。有限元法是解决此类问题最常用的数值方法之一,但因其依赖网格的局限性(三维单元划分困难、网格破裂),导致求解时精度不高或计算效率降低。无网格法是近20年兴起的一种新型数值方法,因其不依赖网格仅依托节点构造高阶连续近似函数的特点,具有独特的优势。在分析层合板结构时,基于位移法的层合板理论包括退化板理论(经典板理论、一阶剪切理论和高阶剪切理论)和三维实体板理论(经典三维板理论、分层板理论)。退化板理论基于不同的近似假设(直法线假设、未考虑横向剪切),直接影响其力学模型对物理模型的近似程度,从而降低了计算精度;三维板理论在处理层合结构时,又大大增加计算时间。本文根据层合板的特殊构造,从层合板的层间位移、应变、应力的连续性要求出发,根据无网格法与有限单元法各自特点,采用面内和横向耦合的离散方法。横向剪切应变及横向正应变利用完全的三维本构关系,满足了层间连续性要求。面内位移场采用二维移动最小二乘(Moving Least Square,MLS)近似,厚度方向位移场采用一维分段线性插值近似,得到了3D位移函数近似新方法MLS-L(Moving Least Square-Linear,MLS-L)。结合Galerkin弱式建立离散系统方程,通过罚函数法施加本质边界条件。使用基于MLS-L近似函数构造的三维层合板无网格法,对不同边界条件、不同厚跨比、不同铺设方式、不同结构形状及不同载荷下的层合板进行了大量的数值计算。采用广义特征值法、Newmark法、模态查重等方法分别对频率、动态响应、模态等振动问题进行数值分析。数值结果表明,本文提供方法对正交层合板的振动问题具有较高精度。
[Abstract]:The laminated plates made of composite materials are widely used in various engineering structures, such as the wings of aircraft and the carriages of high-speed rail because of their light weight, high strength, good dielectric properties, corrosion resistance and so on. The tread of a car and the solar sail of a satellite. The vibration problem of laminated plates has been paid more and more attention with the increasingly demanding requirements of materials in the working environment. Therefore, it is of great engineering significance to study the vibration of laminated plates. Each order frequency, dynamic response and mode are the most basic three problems in the numerical calculation of laminated plate vibration. Finite element method (FEM) is one of the most commonly used numerical methods to solve this kind of problem. However, because of its limitation (3D element division difficulty, mesh rupture), the accuracy of the solution is not high or the computational efficiency is reduced. Meshless method is a new numerical method developed in recent 20 years. It has a unique advantage because it does not rely on mesh to construct high-order continuous approximation functions only by nodes. In the analysis of laminated plate structure, the theory of laminated plate based on displacement method includes degenerate plate theory (classical plate theory, first-order shear theory and high-order shear theory) and three-dimensional solid plate theory (classical three-dimensional plate theory, laminated plate theory). The degenerate plate theory is based on different approximate assumptions (straight normal hypothesis, not considering transverse shear), which directly affects the degree of approximation of the mechanical model to the physical model, thereby reducing the calculation accuracy. The computational time is also greatly increased. According to the special structure of laminated plates, according to the continuity requirements of interlayer displacement, strain and stress of laminated plates, according to the respective characteristics of meshless method and finite element method, the in-plane and transversal coupling discretization methods are adopted in this paper. The transverse shear strain and the transverse positive strain satisfy the requirement of interlaminar continuity by using the complete three dimensional constitutive relation. The in-plane displacement field is approximated by moving least square (MLS) and the displacement field in thickness direction is approximated by one-dimensional piecewise linear interpolation. A new 3D displacement function approximation method, MLS-L (moving least Square-Linear-MLS-L), is obtained. The discrete-time system equation is established by Galerkin weak formula, and the essential boundary condition is applied by penalty function method. A meshless method of three-dimensional laminated plates based on MLS-L approximation function is used. A large number of numerical calculations are carried out for different boundary conditions, different thickness / span ratios, different laying modes, different structural shapes and different loads. The generalized eigenvalue method / Newmark method and the modal check method are used to analyze the frequency, dynamic response and modal vibration respectively. The numerical results show that the method presented in this paper has a high accuracy for the vibration problem of orthogonal laminated plates.
【学位授予单位】：苏州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB33

【共引文献】