基于CUF理论的旋转轴自由振动特性分析

基于卡雷拉统一定理(Carrera unified formulation,CUF)建立了经典边界条件下旋转轴的动力学分析模型。利用CUF框架,将完整的三维动力学模型简化为具有三维求解精度的一维动力学模型。旋转轴的位移场利用二维泰勒公式和改进傅里叶级数进行构建,边界条件则采用罚函数法进行处理,然后结合能量泛函和Hamilton原理对其振动特性进行求解。通过与有限元结果进行对比,验证了此方法的有效性和正确性。在此基础上,研究了边界罚函数因子、几何参数和旋转速度等参数对旋转轴振动特性的影响。该方法具有高效和高精度等特点,为研究旋转轴的振动特性提供了有效的分析手段。

一般边界条件下功能梯度梁三维振动特性研究

基于卡莱拉统一公式(CUF)建立了一般边界条件下功能梯度(FGM)梁的高阶统一动力学模型和分析方法。利用二维泰勒公式对FGM梁截面位移函数进行高阶拟合,经典梁理论可以视为一阶泰勒公式的特殊形式。采用Voigt线性混合模型分别考虑了两种功能梯度材料分布形式:材料属性仅沿宽度或厚度单一方向发生变化;材料属性同时沿宽度和厚度方向发生变化。通过罚函数法将FGM梁的边界条件量化为边界能量的形式,实现了对边界条件的参数化分析,并消除了位移容许函数对边界条件的依赖性。利用瑞利-利兹法和勒让德多项式函数对FGM梁的振动问题进行求解。通过与文献中结果对比,验证了此方法的有效性和正确性。最后,研究了几何尺寸、材料属性和边界条件对FGM梁振动特性的影响规律。

正交各向异性梁结构自由振动分析

针对正交各向异性梁的振动问题,本文基于卡雷拉定理建立了多种边界下正交各向异性梁结构的振动分析模型。将正交各向异性梁结构的位移函数分离为截面和轴向位移2部分。依据卡雷拉定理拟合梁结构的截面位移变形,利用有限元分段插值函数给出梁的轴向位移。结合三维弹性理论建立梁结构的能量表达式,并由最小势能原理推导梁结构3×3阶核心质量矩阵和刚度矩阵。采用划行化列、赋大数等有限元边界施加方法得到特定的动力学方程,进而获得正交各向异性梁的自由振动特性,并开展了多种边界条件下正交各向异性梁结构的数值算例。对比分析表明:本文方法具有较好的收敛速度,计算结果与文献数据和有限元商业软件仿真结果吻合良好。

Effects of Thermo-Mechanical Loads on Aeroelastic Instabilities of Metallic and Composite Panels

Panel flutter phenomena can be strongly affected by thermal loads,and so a refined aeroelastic model is presented.Higher-order shell theories are used as structural models.The aerodynamic forces are described using the Piston theory.The temperature is considered uniform over the thickness of the panel.The aero-thermo-elastic model is derived in the framework of the Carrera unified formulation(CUF),therefore the matrices are expressed in a compact form using the″fundamental nuclei″.Composite and sandwich structures are considered and different boundary conditions are taken into account.The effects of the thermal load on the aeroelastic behavior are investigated.

Multilayered plate elements with node-dependent kinematics for electro-mechanical problems

In the present work,a new class of finite elements(FEs)for the analysis of composite and sandwich plates embedding piezoelectric skins and patches is proposed.By making use of node-by-node variable plate theory assumptions,the new finite element allows for the simultaneous analysis of different subregions of the problem domain with different kinematics and accuracy,in a global/local sense.As a consequence,the computational costs can be reduced drastically by assuming refined theories only in those zones/nodes of the structural domain where the resulting strain and stress states,and their electro-mechanical coupling present a complex distribution.The primary advantage is that no ad-hoc techniques and mathematical artifices are required to mix the fields coming from two different and kinematically incompatible adjacent elements,because the plate structural theory varies within the finite element itself.In other words,the structural theory of the plate element is a property of the FE node in this present approach,and the continuity between two adjacent elements is ensured by adopting the same kinematics at the interface nodes.The finite element arrays of the generic plate element are formulated in terms of fundamental nuclei,which are invariants of the theory approximation order and the modeling technique(Equivalent-Single-Layer,Layer-Wise).In this work,the attention is focused on the use of Legendre polynomial expansions to describe the through-the-thickness unknowns to develop advanced plate theories.Several numerical investigations,such as composite and sandwich multilayered plates embedding piezoelectric skins and patches with various load,boundary conditions,and piezoelectric material polarizations,are carried out to validate and demonstrate the accuracy and efficiency of the present plate element,including comparison with various closed-form and FE solutions from the literature.

Advanced modeling of embedded piezo-electric transducers for the health-monitoring of layered structures

The present paper presents an innovative approach for the numerical modeling of piezo-electric transducers for the health-monitoring of layered structures.The numerical approach has been developed in the frameworks of the Carrera Unified Formulation.This computa-tional tool allows refined numerical models to be derived in a unified and efficient fashion.The use of higher-order models and the cap-ability to connect different kinematic models using the node-depen-dent kinematic approach has led to an efficient modeling technique for global-local analysis.This approach can refine the model only in those regions where it is required,e.g.,the areas where piezo-electric transducers are placed.The model has been used to study embedded and surface-mounted sensors.The accuracy of the pre-sent model has been verified by comparing the current results with numerical and experimental data from the literature.Different mod-eling solutions have been developed,mixing one-,two-and threedimensional finite elements.The results show that the use of the present modeling technique allows the computational cost to be reduced with respect to the classical approaches preserving the ccuracy of the results in the critical areas.

A layer-wise MITC9 finite element for the freevibration analysis of plates with piezo-patches

The present article considers the free-vibration analysis of plate structures with piezoelectric patches by means of a plate finite element with variable through-the-thickness layer-wise kinematic.The refined models used are derived from Carrera’s Unified Formulation(CUF)and they permit the vibration modes along the thickness to be accurately described.The finite-element method is employed and the plate element implemented has nine nodes,and the mixed interpolation of tensorial component(MITC)method is used to contrast the membrane and shear locking phenomenon.The related governing equations are derived from the principle of virtual displacement,extended to the analysis of electromechanical problems.An isotropic plate with piezoelectric patches is analyzed,with clamped-free boundary conditions and subjected to open-and short-circuit configurations.The results,obtained with different theories,are compared with the higher-order type solutions given in the literature.The conclusion is reached that the plate element based on the CUF is more suitable and efficient compared to the classical models in the study of multilayered structures embedding piezo-patches.

Buckling of thin-walled beams by a refined theory

The buckling of thin-walled structures is presented using the 1D finite element based refined beam theory formulation that permits us to obtain N-order expansions for the three displacement fields over the section domain.These higher-order models are obtained in the framework of the Carrera unified formulation(CUF).CUF is a hierarchical formulation in which the refined models are obtained with no need for ad hoc formulations.Beam theories are obtained on the basis of Taylor-type and Lagrange polynomial expansions.Assessments of these theories have been carried out by their applications to studies related to the buckling of various beam structures,like the beams with square cross section,I-section,thin rectangular cross section,and annular beams.The results obtained match very well with those from commercial finite element softwares with a significantly less computational cost.Further,various types of modes like the bending modes,axial modes,torsional modes,and circumferential shell-type modes are observed.

基于一维高阶理论的矿井提升机阶梯主轴静力分析（英文）

目的:研究基于Carrera通用表达式的一维高阶理论,将其应用于矿井提升机主轴的力学特性分析,针对矿井提升的特殊工况对主轴模型进行改进,并探究该改进模型在工况监测中的可用性。创新点:基于Carrera一维高阶理论,建立提升机主轴的一维高阶模型;根据矿井提升的特殊工况对主轴模型进行改进,得到改进的主轴一维高阶模型。方法:1.引入基于Carrera通用表达式的一维高阶理论,克服传统梁理论的局限性和三维有限元法计算经济性差等问题;2.通过理论计算、软件仿真和现场试验(图14和15),验证改进的主轴一维高阶模型的有效性和可用性。结论:1.基于Carrera通用表达式的一维高阶理论模型能够以较少的计算量得出与ANSYS三维实体模型相近的结果;2.改进的提升机主轴一维高阶模型能够准确地监测矿井提升系统的工况。