面内功能梯度三角形板等几何面内振动分析

Isogeometric in-Plane Vibration Analysis of Functionally Graded Triangular Plates

基于平面应变理论,利用等几何有限元方法分析了弹性边界条件下面内功能梯度三角形板的面内振动特性.板的材料属性沿厚度方向呈均匀分布,而在面内方向呈任意指数梯度变化.采用非均匀有理B样条(NURBS)基函数对三角形结构进行等几何建模和位移描述,实现了三角形板几何设计和振动分析的无缝衔接.在三角形板边界上引入虚拟弹簧约束并通过调节虚拟弹簧刚度,实现任意边界条件的施加.通过不同的单元细化方案和对比算例,验证了等几何方法的灵活性、准确性和快速收敛性.系统研究了边界条件、材料属性和几何参数对三角形板振动特性的影响.同时给出了弹性边界条件下面内功能梯度三角形板的振动特性解,具有重要参考价值.

The in⁃plane vibration of the triangular plates of in⁃plane functionally graded(IFG)materials based on the plane stress theory was investigated by means of isogeometric analysis(IGA).The material of the triangular plate is homogenous in the thickness direction,but func⁃tionally graded along the in⁃plane direction.The geometry and displacement field of the consid⁃ered plate were constructed with the non⁃uniform rational B⁃splines(NURBS)basis functions,then a seamless integration of the geometric design and the vibration characteristic analysis of the triangular plate was realized.The arbitrary boundary conditions of the triangular plate were obtained through adjustment of the stiffness of artificial springs introduced into the boundary of the triangular plate.The flexibility,high accuracy and quick convergency of the proposed meth⁃od were verified through different refinements and results comparison.Finally,effects of boundary conditions,material properties and geometry parameters were investigated systemati⁃cally.The vibration solutions of many kinds of triangular plates of in⁃plane functionally graded materials with elastic boundary conditions were given.The work provides a good reference for engineering application.