摘要
桁架材料的连续介质等效模型的研究已有相当基础,而工程中桁架材料往往以类板结构形式出现,其变形表现出明显的弯曲特征。将类板桁架材料采用弯曲板模型模拟,研究合理的方法确定等效板模型的刚度具有重要意义。本文在基于Kirchhoff假定的小挠度薄板弹性理论框架下,研究了类板桁架材料的等效弯曲薄板模型,提出了确定薄板模型等效刚度的基于Dirichlet位移边界条件的代表体元法,给出了确定各刚度系数所对应的代表体元的边界位移形式。具体计算了几种典型形式桁架板的等效刚度,并采用有限元离散模型和实验技术分析了桁架板在一定的边界约束和荷载作用下的响应,并与等效板模型的分析结果进行了对比。结果表明,在响应分析中,具有等效刚度的薄板模型可准确模拟类板桁架材料;连续介质板等效刚度计算的积分法不能给出准确的桁架板等效刚度,而基于Dirichlet位移边界条件的代表体元法获得的等效板的刚度具有很高的精度。
The effective properties of truss lattice material based on the effective continuum model have been widely investigated. Moreover, truss material is often used as plate-like structure and shows remarkable bending characteristics in deformation. It is of great significance to describe the plate-like truss lattice material with a plate model and to examine a suitable method to achieve the effective stiffness of the plate model. The purpose of this paper is to introduce an effective thin plate model which follows the theory of elastic-thin-plates with small deflection, based on the Kirchhoff assumption for plate-like truss lattice material, and to recommend a method to calculate the effective stiffness of the plate model. Specifically, the representative volume element （RVE） method, based on Dirichlet boundary conditions, was chosen as an effective method. The corresponding Dirichlet boundary conditions have been derived in detail before the effective thin plate stiffness of some typical truss lattice material plates is performed. The responses of different truss lattice effective thin plates under some boundary conditions and loading cases are compared with finite elements （FE） solutions and experimental observations. The results show that thin plate model with effective stiffness can simulate truss lattice material in response analysis precisely and that the effective plate stiffness from RVE, based on Dirichlet boundary conditions, is accurate, while, the integral method, based on the effective continuum model, cannot provide an accurate description of the effective stiffness.
出处
《计算力学学报》
EI
CAS
CSCD
北大核心
2007年第6期763-767,共5页
Chinese Journal of Computational Mechanics
基金
国家自然科学基金重点项目(10332010)
国家重点基础研究计划(973)(2006CB601205)
"新世纪优秀人才"资助计划(2004)
国家自然科学创新群体基金(10421202)资助项目
关键词
桁架材料
桁架板
等效刚度
代表体元法
truss lattice material
truss plate
effective stiffness
representative volume element method
