Triangular Differential Quadrature Method in Bending Analysis of Triangular Symmetric Laminated Plates

The main advantage of triangular differential quadrature method in numerical simulations of problems in triangular domain is that it needs very few grid points compared to those of low order methods. In the current work, the method is implemented to analyze the bending behavior of relatively thick triangular composite plates based on the concept of first-order shear deformation theory. A set of triangular symmetric laminated plates with various lay-ups, length to thickness ratios, and boundary conditions is considered. The results are discussed in detail and compared with those obtained from finite element method of analysis using ANSYS package.     

Bending Analysis of Classical Symmetric Laminated Composite Plates by the Strip Element Method

A new formulation of strip element method based on classical laminated plate theory is derived for the bending analysis of laminated composite plates. In this method, an infinite-length plate is first considered and is discretized into a set of strip elements in the width direction. The principle of minimum potential energy is applied to obtain the ordinary differential equations, which are functions of only the coordinate in the length direction. These differential equations can then be solved analytically. The boundary conditions on the length coordinate direction are finally used to determine the deflection distribution in the plate. The strip element solutions are presented for a rectangular laminated composite plate with various boundary conditions and load cases. The solutions are compared with those of the Rayleigh-Ritz method, and very good agreement is obtained.     

U形槽板多工步折弯方法及回弹预测

分析对比了大型U形槽板的2种折弯成形方式,取U形槽板的小件进行多工步折弯回弹的有限元模拟并进行了相应的物理实验,得出了回弹角度预测值,提出在多工步折弯回弹有限元模拟中要注意的问题,为大型U形槽板的折弯成形生产提供了参考。     

Nonlinear Viscoelastic Response of Unidirectional Polymeric Laminated Composite Plates Under Bending Loads

Nonlinear bending analysis of polymeric laminated composite plate is examined considering material nonlinearity for viscoelastic matrix material through a Micro–macro approach. The micromechanical Simplified Unit Cell Method (SUCM) in three-dimensional closed-form solution is used for the overall behavior of the unidirectional composite in any combination of loading conditions. The elastic fibers are transversely isotropic where Schapery single integral equation in multiaxial stress state describes the matrix material by recursive-iterative formulation. The finite difference Dynamic Relaxation (DR) method is utilized to study the bending behavior of Mindlin annular sector plate including geometric nonlinearity under uniform lateral pressure with clamped and hinged edge constraints. The unsymmetrical laminated plate deflection is predicted for different thicknesses and also various pressures in different time steps and they are compared with elastic finite element results. As a main objective, the deflection results of viscoelastic laminated sector plate are obtained for various fiber volume fractions in the composite system.     

拉挤成型复合材料板桩抗弯刚度简化计算

将折线型截面复合材料板桩整体刚度表示成翼缘和腹板刚度之和,基于层合板理论分层计算翼缘和腹板的局部刚度,然后提出整体结构抗弯刚度和抗剪刚度的简化计算公式,因此结构在弯曲荷载作用下的位移理论值可采用Timoshenko方程获得。开展拉挤复合材料板桩四点弯试验,将测量的荷载-位移曲线与理论值进行对比,表明本文推导的刚度计算公式在弹性范围内具有较好的精度,其中跨高比更大的试件理论与试验值更接近。该理论公式也可用于计算Z型、槽型、工字型等截面复合材料结构的刚度和位移。     

Q345B帆形板渐进弯曲加载路径研究

目的 提高渐进弯曲成形中厚高强钢板帆形件的精度,基于最小能量法提出不同加载路径并进行实验对比,以获取满足精度需求的加载路径。方法 选用Q345B为实验材料,进行不同加载路径的单层和多层渐进弯曲成形实验,使用视觉检测系统获取样本形状数据。分析不同加载路径的缺陷影响,并在沿x轴截面、沿y轴截面和沿x=y截面上对不同加载路径的成形形状和成形误差进行对比分析。进一步引入辅助支撑与辅助加热装置进行实验,对在有无辅助支撑和有无辅助加热条件下的结果进行分析。结果 在“由里到外”的加载路径下,单层与多层成形的平均误差分别为8.5 mm与6.5 mm;在“由外到里”的加载路径下,单层与多层成形的平均误差分别为3.2 mm与2.7 mm。在“由外到里”加载路径多层成形的基础上引入辅助支撑后平均误差降为1.16 mm。在增加辅助支撑的基础上再增加辅助加热(将板材加热到300℃),板材平均误差降为0.8 mm。结论 “由外到里”加载路径为更好的加载路径。同时增加辅助支撑与辅助加热可进一步改善成形缺陷、提高成形精度。     

Static Response of Geometrically Nonlinear Laminated Composite Plates Having Uncertain Material Properties

The effect of uncertainty in material properties on the transverse bending of laminated composite plate is investigated. The transverse shear and large rotations have been included in the system equation in the framework of higher order shear deformation theory. The analysis uses Green–Lagrange nonlinear strain displacement equations to model geometric nonlinearity. The stochastic finite element analysis is performed using a direct iteration approach to handle deterministic geometric nonlinearity and perturbation approach to handle the randomness in the material properties. Mean and variance of the transverse deflection have been obtained by employing a C⁰ isoparametric nonlinear finite element model.     

Moment Distribution around Circular/Elliptical/Triangular Cutouts in Infinite Symmetric Laminated Plate

In this article, a general solution for moment distribution around a circular/elliptical/triangular shaped hole in a laminated composite plate subjected to a bending/twisting moment at infinity is presented. The numerical results are obtained for graphite/epoxy, glass/epoxy, boron/epoxy, etc. The effect of loading factor, stacking sequence, material parameters, and hole geometry on moment distribution is studied for cross ply and angle ply laminates. The results are compared with existing literature and found to be in good agreement.     

Exact Solutions for the Analysis of Piezoelectric Fiber Reinforced Composites as Distributed Actuators for Smart Composite Plates

Performance of a layer of piezoelectric fiber reinforced composite (PFRC) material as the distributed actuator for smart composite plates has been investigated in this paper. The investigation is performed by finding the exact solutions for static analysis of simply supported symmetric and anti-symmetric cross-ply laminated plates integrated with a layer of PFRC material. The results suggest the potential use of PFRC materials for the distributed actuators of smart structures with both thick and thin substrate composite plates.     

Exact Solutions for the Analysis of Piezoelectric Fiber Reinforced Composites as distributed Actuators for Smart Composite Plates

Performance of a layer of piezoelectric fiber reinforced composite (PFRC) material as the distributed actuator for smart composite plates has been investigated in this paper. The investigation is performed by finding the exact solutions for static analysis of simply supported symmetric and anti-symmetric cross-ply laminated plates integrated with a layer of PFRC material. The results suggest the potential use of PFRC materials for the distributed actuators of smart structures with both thick and thin substrate composite plates.     

正交叠层机织布整体穿刺工艺的纤维弯曲伸长机理

分析了正交叠层机织布整体穿刺工艺机织布与钢针的相互作用，提出并建立了纤维的弯曲伸长及伸长断裂模式，讨论了影响纤维弯曲伸长的结构参数。通过理论分析和试验结果说明，绕针弯曲伸长断裂是Z向钢针直径和Z向距比值X的函数，为减少整体穿刺的纤维伸长断裂应选取较小的X比值。     

Ultralarge Bending Strain and Fracture‐Resistance Investigation of Tungsten Carbide Nanowires

Hard tungsten carbide (WC) with brittle behavior is frequently applied for mechanical purposes. Here, ultralarge elastic bending deformation is reported in defect‐rare WC [0001] nanowires; the tested bending strain reaches a maximum of 20% ± 3.33%, which challenges the traditional understanding of this material. The lattice analysis indicates that the dislocations are confined to the inner part of the WC nanowires. First, the high Peierls–Nabarro barrier hinders the movement of the locally formed dislocations, which causes rapid dislocation aggregation and hinders long‐range glide, resulting in a dense distribution of the dislocation network. In this case, the loading is dispersed along multiple points, which is then balanced by the complex internal mechanical field. In the compressive part, the possible dislocations predominantly emerge in the (0001) plane and mainly slip along the axial direction. The disordered shell first forms at the tensile side and prevents the generation of nanocracks at the surface. The novel lattice kinetics make WC nanowires capable of substantial bending strain resistance. Analytical results of the force–displacement (F–d) curves based on the double‐clamped beam model exhibit an obvious nonlinear elastic characteristic, which originates fundamentally from the lattice anharmonicity under moderate stress.     

高温中和高温后LVL木纤维复合材的抗弯性能

为研究LVL木纤维复合材在高温中和高温后的抗弯性能,对104个试样进行了温度在20~225℃下的三点静态抗弯测试。研究结果表明,随着温度的升高,高温中和高温后的抗弯强度、抗弯弹性模量、延性系数均明显减小;相对于高温中的试样,高温后的抗弯强度和抗弯弹性模量均明显较高,而延性系数则较低。根据回归分析,提出了LVL在高温中和高温后的抗弯强度与温度的关系模型,该模型预测结果与实测值吻合良好。     

Three-Dimensional Solutions of Functionally Graded Piezo-Thermo-Elastic Shells and Plates Using a Modified Pagano Method

A modified Pagano method is developed for the three-dimensional (3D) coupled analysis of simply-supported, doubly curved functionally graded (FG) piezo-thermo-elastic shells under thermal loads. Four different loading conditions, applied on the lateral surfaces of the shells, are considered. The material properties of FG shells are regarded as heterogeneous through the thickness coordinate, and then specified to obey an exponent-law dependent on this. The Pagano method, conventionally used for the analysis of multilayered composite elastic plates/shells, is modified to be feasible for the present analysis of FG piezo-thermo-elastic plates/shells. The modifications include that a displacement-based formulation is replaced by a mixed formulation, a set of the complex-valued solutions of the system equations is transferred to the corresponding set of real-valued solutions, a successive approximation (SA) method is adopted and introduced in the present analysis, and the propagator matrix method is developed for the heat conduction analysis and the coupled piezo-thermo-elastic analysis of the FG shells. The influence of the material-property gradient index on the field variables, induced in the FG piezo-thermo-elastic shells and plates under the thermal load, is studied.     

弯曲速度对弯管壁厚变化的影响

采用不同弯曲速度对5A06和1Cr18NiTi管进行了旋转弯曲试验和有限元模拟。分析后指出,弯曲速度对弯曲内侧管壁变形影响较大,弯曲内侧切向应力、应变及管壁增厚率均随弯曲速度增大而增大。同时,内侧管壁增厚对弯曲速度的敏感性具有随原始壁厚的增大而减小的变化趋势。薄壁管在过大弯曲速度下成形时,内侧因材料流动受阻滞易发生失稳起皱。     

Computation of Laminated Composite Plates using Integrated Radial Basis Function Networks

This paper reports a meshless method, which is based on radial-basis-function networks (RBFNs), for the static analysis of moderately-thick laminated composite plates using the first-order shear deformation theory. Integrated RBFNs are employed to represent the field variables, and the governing equations are discretized by means of point collocation. The use of integration rather than conventional differentiation to construct the RBF approximations significantly stabilizes the solution and enhances the quality of approximation. The proposed method is verified through the solution of rectangular and non-rectangular composite plates. Numerical results obtained show that the method achieves a very high degree of accuracy and a fast convergence rate.     

一组椭圆形截面吊臂折弯间隙、步进及折弯刀数计算公式

目的研究椭圆形截面吊臂折弯时折弯间隙和折弯步进的关系。方法构建了一组吊臂折弯间隙、步进及折弯刀数的计算公式。结果结果表明,通过该公式所得折弯工艺参数与实践较吻合,同时,折弯效率也可以得到极大提高,以180 t产品为例,增大折弯步进后,折弯效率提高了20.3%~56.4%。结论建立了折弯间隙、折弯步进及折弯刀数的数学模型,可以据此得出所需的最优工艺参数,该模型对实际生产具有很好的工艺指导和支撑作用,可极大提高生产效率。     

复合材料层合板自由振动的薄板样条无网格解

无网格全局配点法分为多项式配点法和径向基函数配点法,国内外很多文献利用径向基函数配点法对复合材料层合板进行了分析。利用一阶剪切变形理论和基于薄板样条径向基函数的无网格配点法计算了复合材料层合板自由振动的固有频率和振型。研究了薄板样条径向基函数中形状参数的选取和本工作方法的收敛性。结果表明:形状参数m=3时收敛性最好,计算精度最高。将本工作计算结果与文献中的实验结果进行了对比,验证了本文方法的精度和效率。     

《压电层合板的振动主动控制》

利用一阶剪切变形理论推导压电层合板的抗弯刚度,由Hamilton变分原理建立压电层合板的有限元模型,采用模态叠加方法对有限元模型降阶。在应变最大处配置制动器和传感器,并采用二次线性控制的独立模态空间控制法来进行板结构的主动控制。数值算例验证了这种力学建模方法和控制方法的有效性。     

Nonlinear Symmetric Free Vibration Analysis of Super Elliptical Isotropic Thin Plates

Nonlinear symmetric free vibration analyses are first presented for super elliptical isotropic thin plates with simply supported edge and clamped edge based on classical plate theory. Approximate solutions of super elliptical thin plates are obtained by Ritz method, and the validity can be confirmed by comparison with related researchers’ results. Numerical results confirm that the characteristics of nonlinear vibration behaviors are significantly influenced by different boundary conditions, vibration amplitudes, the power of the super ellipse, as well as ratio of major to minor axis.