Pure bending of simply supported circular plate of transversely isotropic functionally graded material

This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. The analytical expressions of axial force, bending moment and displacements are then deduced through integration. And then, stress functions are employed to solve problems of transversely isotropic functionally graded circular plate, with the integral constants completely determined from boundary conditions. An elasticity solution for pure bending problem, which coincides with the available solution when degenerated into the elasticity solutions for homogenous circular plate, is thus obtained. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a simply supported circular plate of transversely isotropic functionally graded material (FGM).

MECHANICAL ANALYSIS OF CYLINDERS BEING UPSET BETWEEN SPHERICAL CONCAVE PLATEN AND CONCAVE SUPPORTING PLATE

Mechanical analysis of cylinders being upset between spherical concave platen and concave supporting plate is conducted. Rigid-plastic mechanical models for cylinders are presented. When the ratio of height to diameter, is larger than 1, there exists two-dimensional tensile stress in the deformed body, when the ratio is smaller than 1, there exists shear stress in static hydraulic zone. The former breaks through the theory that there is three-dimensional compressive stress irrespective of any ratio of height to diameter. The latter satisfactorily explains the mechanism of layer-like cracks in disk-shaped forgings and the flanges of forged gear axles. The representation of the two models makes the upsetting, theory into correct and perfect stage.

VIBRATIONS OF RECTANGULAR PLATES SUPPORTED AT CORNER POINTS

This paper discusses by energy theorem the methodof approximate computation for the lowest eigenfrequencies of rechmguhir plates,on which there are symmetrical concentrated masses,supported at corner points,In the case of seseral concentrated masses,by using the prineiple of superposition we mayfiml the reduneed coefficients of masses comveniently.llence we can louain the lowest eigenfrequencies of thin plates.In the paper a good mamy mmerical caleuhting eximples are inustrated

THE DYNAMIC PLASTIC BEHAVIOR OF A SIMPLY SUPPORTED CIRCULAR PLATE IN A DAMPING MEDIUM WITH FINITE-DEFLECTIONS

A theoretical analysis is presented for the dynamic plastic behavior of a simply supported rigid, perfectly plastic circular plate in damping medium with finite-deflections subjected to a rectangular pressure pulse. Analytical solutions of every moving stage under both medium and high loads are developed.

TRANSVERSE VIBRATION OF RECTANGULAR PLATES ELASTICALLY SUPPORTED AT POINTS ON EDGES

This paper studies transverse vibration of rectangular plates with two opposite edges simply supperted other two edges arbitrarily supported and free edges elaslically supported at points,A highly accurate solution is presented for calculating inherent frequencies and mode shape of rectangular platen elaslically supported at points. The number and location of these points on free edges may be completely arbitrary. This paper uses impulse function to represent reaction and moment at points. Fourter series is used to expand the impulse function along the edges. Characteristic equations satisfying all boundary conditions are given.Inherent frequencies and mode shape with any accutacy can be gained.

AN EXACT SOLUTION FOR THE BENDING OF POINT-SUPPORTED ORTHOTROPIC RECTANGULAR THIN PLATES

A closed series solution is proposed for the bending of point-supported orthotropic rectangular thin plates. The positions of support points and the distribution of transverse loadare arbitrary. If the number of simply supported points gradually increases the solution can infinitely approach to Navier's solution. For the square plate simply supported on the middle of each edge and free at each corner, the results are very close to the numerical solutions in the past.

Element-free Galerkin method for free vibration of rectangular plates with interior elastic point supports and elastically restrained edges

The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.

Thermoelastic vibrations in a thin elliptic annulus plate with elastic supports

In this study, integral operational methods are used to investigate the thermally induced transverse vibration of a thin elliptic annulus plate with elastic supports at both radial boundaries.The axisymmetric temperature distribution is determined by the heat conduction differential equation and its corresponding boundary conditions by employing a unified integral transform technique by use of Mathieu functions and modified Mathieu functions. The solution of thermally induced vibration of the plate with both ends encased with elastic supports is obtained by employing an integral transform for double Laplace differential equation. The thermal moment is derived on the basis of temperature distribution, and its stresses are obtained based on resultant bending moments per unit width. The numerical calculations of the distributions of the transient temperature and its associated stress distributions are shown in the figures.

NONLINEAR BENDINGS FOR THE ORTHOTROPIC RECTANGULAR THIN PLATES UNDER VARIOUS SUPPORTS

In this paper, the nonlinear bandings for the orthotropic rectangular thin plates under various supports are studied.The uniformly valid asymptotic solutions of the displacement ? and stress function φ are derived by the perturbation offered in [1].

BENDING OF UNIFORMLY LOADED RECTANGULAR PLATES WITH TWO ADJACENT EDGES CLAMPED, ONE EDGE SIMPLY SUPPORTED AND THE OTHER EDGE FREE

In this paper, an exact solution for an uniformly loaded rectangular plate with two adjacent edges clamped, one edge simply supported and the other edge free, was given by using the concept of generalized simply supported edges and superposition method. The numerical results were given for the deflections along the free edge and bending moments along the clamped edges of a square plate.

AN ANALYTICAL SOLUTION OF TRANSVERSE VIBRATION OF RECTANGULAR PLATES SIMPLY SUPPORTED AT TWO OPPOSITE EDGES WITH ARBITRARY NUMBER OF ELASTIC LINE SUPPORTS IN ONE WAY

This paper presents presents a new analytical solution of transverse vibration ofrectangular plaies simply supported at two opposite edges with arbitrary number ofelastic line supports in one way. The reaction forces of the elastic line supports areregarded as foe unknown external forces acted on the plate. The analytical solution ofthe differential equation of motion of the rectangular plate, which includes theunknown reaction forces. is gained. The frequency' equation is derived by using thelinear relationships between the reaction forces of the elastic line supports and thetransverse displacements of the plale along the elastic line supports. Therepresentations of foe frequency equation and the mode shape functions are differentfrom those obtained by other methods.

THE APPLICATION OF WEINSTEIN-CHIEN′S METHOD——THE UPPER AND LOWER LIMITS OF FUNDAMENTAL FREQUENCY OF RECTANGULAR PLATES WITH EDGES ARE THE MIXTURE OF SIMPLY SUPPORTED PORTIONS AND CLAMPED PORTIONS

In this paper, the method of relaxed boundary conditions is applied to rectangular plates with edges which are a sort of the mixture of simply supported portions and clamped portions, so that the lower limit of fundamental frequency of such plates is evaluated. A kind of polynomial satisfying the displacement boundary conditions is designed, os that it is enabled to evaluate the upper limit of fundamental frequency by Ritz' method. The practical calculation examples solved by these methods have given satisfactory results. At the end of this paper, it is pointed out that the socalled exact solution of such plates usually evaluated by the force superposition method is essentially a kind of lower limit of solution, if the truncated error of series which occurs in actual calculation is considered.

Influence of Support Conditions on the Hydroelastic Behaviour of Floating Thick Elastic Plate

The hydroelastic response of very large floating structures (VLFS) under the action of ocean waves is analysed considering the small amplitude wave theory. The very large floating structure is modelled as a floating thick elastic plate based on Timoshenko- Mindlin plate theory, and the analysis for the hydroelastic response is performed considering different edge boundary conditions. The numerical study is performed to analyse the wave reflection and transmission characteristics of the floating plate under the influence of different support conditions using eigenfunction expansion method along with the orthogonal mode-coupling relation in the case of finite water depth. Further, the analysis is extended for shallow water depth, and the continuity of energy and mass flux is applied along the edges of the plate to obtain the solution for the problem. The hydroelastic behaviour in terms of reflection and transmission coefficients, plate deflection, strain, bending moment and shear force of the floating thick elastic plate with support conditions is analysed and compared for finite and shallow water depth. The study reveals an interesting aspect in the analysis of thick floating elastic plate with support condition due to the presence of the rotary inertia and transverse shear deformation. The present study will be helpful for the design and analysis of the VLFS in the case of finite and shallow water depth.

Data Mining Based Research of Development Direction of Waist Protection Equipment

[Objectives]To explore the trend of brands towards the design of waist protection products through data mining,and to provide reference for the design concept of the contour of waist protection pillow.[Methods]The structural design information of all waist protection equipment was collected from the national Internet platform,and the data were classified and a database was established.IBM SPSS 26.0 and MATLAB 2018a were used to analyze the data and tabulate them in Tableau 2022.4.After the association rules were clarified,the data were imported into Cinema 4D R21 to create the concept contour of waist protection pillow.[Results]The average and standard deviation of the single airbag design were the highest in all groups,with an average of 0.511 and a standard deviation of 0.502.The average and standard deviation of the upper and lower dual airbags were the lowest in all groups,with an average of 0.015 and a standard deviation of 0.120;the correlation coefficient between single airbag and 120°arc stretching was 0.325,which was positively correlated with each other(P<0.01);the correlation coefficient between multiple airbags and 360°encircling fitting was 0.501,which was positively correlated with each other and had the highest correlation degree(P<0.01).[Conclusions]The single airbag design is well recognized by companies,and has received the highest attention among all brand products.While focusing on single airbag design,most brands will consider the need to add 120°arc stretching elements in product design.At the time of focusing on multiple airbag design,some brands believe that 360°encircling fitting elements need to be added to the product,and the correlation between the two is the highest among all groups.

四边不同支承条件下矩形板的结构计算

采用带补充项的傅立叶级数作为挠度函数,针对四边不同支承矩形薄板,推导了确定待定系数的方程组,给出可处理简支边、固支边和自由边任意组合条件下统一的结构计算公式.探讨了集中荷载作用处弯矩级数解不收敛的处理办法,以及双向板简化为单向板需要达到的长宽比问题.结果表明,集中荷载作用处的弯矩,可采用挠度值按中心差分公式进行计算,差分步长可取10 mm.对边支承对边自由板及一边固支三边自由板,可视作单向板.当四边支承板的长宽比达到2∶1、2.5∶1及4.5∶1时,可分别简化为两端固支、一端简支一端固支及两端简支单向板.三边支承一边自由板长宽比达到1∶1及2∶1时,可分别简化为两端固支(及一端简支一端固支)及两端简支单向板;长宽比达到6∶1时,可简化为悬臂单向板.两邻边支承两邻边自由板若要简化为悬臂单向板,在两支承边为固支时,长宽比需要达到2∶1;在支承边为一边简支一边固支时,长宽比要达到1.5∶1.

改进YOLOv5s的采煤机滚筒与支架护帮板干涉状态智能识别

针对综采工作面液压支架护帮板处于未收回异常状态导致采煤机滚筒与护帮板干涉问题,提出一种改进YOLOv5s的采煤机滚筒与液压支架护帮板干涉状态智能识别方法。运用课题组前期提出的基于边界约束和非线性上下文正则化的去雾去尘方法对视频图像进行清晰化处理,提高综采工作面监控视频图像质量;对YOLOv5s模型进行改进,通过将YOLOv5s主干网络中的普通卷积Conv替换为分类效果更佳的Ghost卷积,减少了模型的参数数量,提高了模型识别速度,同时引入坐标注意力机制,提高了模型对护帮板和滚筒特征提取能力,从而提高模型识别精确率。运用软非极大值抑制算法(Soft-NMS)的锚框筛选方法,减少因护帮板重叠而发生漏检问题。针对采煤机滚筒与液压支架护帮板干涉状态判定问题,提出液压支架护帮板与采煤机滚筒锚框重合度的判定方法。运用本文改进YOLOv5s模型与YOLOv5s、YOLOv3-tiny模型进行对比分析,结果表明:本文方法与原模型相比的识别精确率提高了约8.1%,GFLOPs降低1.86倍;mAP@.5达到97.2%、平均识别速度为检测时间为5.9 ms。运用本文方法对煤矿实际综采工作面采煤机滚筒与液压支架护帮板视频图像进行干涉状态识别试验验证,结果表明:对采煤机滚筒与液压支架护帮板干涉状态识别准确率为96%。

四边固支板在均布荷载作用下的剪力分布规律

沉箱底板抗剪往往需要控制底板厚度,而现有剪力分布规律研究较少,针对此问题采用有限元方法进行不同组合工况的计算,研究四边固支板在均布荷载作用下,板边最大剪力分布以及最大剪力随板厚、边长、长宽比的变化关系,得出最大剪力与平均剪力之比的一般规律。研究结果表明:板边剪力分布呈类抛物线形,板边最大剪力值小于弹性薄板理论计算的最大剪力值;相同尺度和荷载情况下,矩形板厚度增大其板边最大剪力值将有所减小;矩形板尺度增大,板边最大剪力值将迅速增大且最大剪力与平均剪力之比也有所增大;对于常用沉箱纵横隔墙间距和底板厚度,板边最大剪力与平均剪力之比通常为1.3~1.6。总结剪力分布与仓格尺度的关系,旨在为类似工程设计提供参考。

全框支厚板转换斜交高层结构抗震性能研究

设计制作1∶15全框支厚板转换高层结构的微粒混凝土振动台试验模型,进行7度小震、中震、大震以及8度大震作用下单向、双向、三向共计44组工况的振动台试验,研究动力特性、动力放大系数、层间位移角等性能指标,揭示结构塑性损伤发展机制,进一步采用数值模型研究上部塔楼斜交角度对结构抗震性能的影响。结果表明,全框支厚板转换高层结构具有优良的抗震性能,模型结构经历8度大震后,全框支层未见明显裂缝,处于轻微损坏与完好之间,塔楼剪力墙底部和连梁端部裂缝发生明显,薄弱部位集中在3~10层;模型结构动力放大系数沿高度呈“S”形分布模式,在塔楼顶部放大明显,而全框支层的动力放大系数在不同烈度地震作用下始终处于1~2之间;塔楼斜交角度对此类结构体系动力特性和动力响应的影响很小,全框支层均能对上部不同斜交角度的塔楼起到充分的约束作用,上部塔楼承担绝大部分地震输入能量,全框支层的动力放大系数和动力响应均远低于上部塔楼,全框支厚板转换斜交高层结构体系能够实现“强全框支层弱塔楼”设计理念。

厚板转换全框支剪力墙结构振动台试验抽层简化模型设计与分析

为研究厚板转换全框支剪力墙结构的整体抗震性能,并检验该结构转换厚板的有效性,在重庆大学土木工程学院振动台实验室开展了缩尺模型结构的模拟地震振动台试验,试验对象为某36层车辆段上盖建筑。本文阐述了厚板转换全框支剪力墙结构振动台试验中模型的设计过程;介绍了测点布置与加载方案;对比分析了不同抽层简化方案对结构的影响。研究结果表明,对于厚板转换全框支剪力墙结构,抽层后依据刚度与强度等效原则调整构件截面能有效降低简化模型与原型的误差;抽层起始位置应被保证距离试验重点研究楼层不低于3层;连续抽层层数为1层时误差最小,建议选择连续抽层层数为1层。

矿用单元式液压支架立柱“井”形防冲吸能构件特性分析

为了解决目前煤矿井下巷道支护设备和支护材料在冲击地压作用下发生损坏破坏和失效的问题,设计研发了一种新型多肋板吸能构件。首先,根据防冲支架吸能构件的作用原理,明确了吸能构件的设计要求,提出了一种多肋板型吸能构件,对吸能构件的构型和截面形状展开了结构设计,给出了多肋板型吸能构件尺寸图与三维模型图;基于简化的超折叠单元理论剖析了“井”形管的能量耗散途径,推导出了“井”形管的平均支反力预测公式;其次,采用数值模拟方法对多肋板型吸能构件吸能特性展开了仿真研究,并探究了肋板厚度和不同材料对多肋板型吸能构件的吸能性能的影响,得出了肋板厚度和材料显著影响吸能性能的结论。最后,利用MATLAB的遗传算法进行了优化,利用参数优化结果,重新设计了多肋板型吸能构件,并进行了仿真试验,将仿真试验与压溃试验的结果进行对比分析。分析表明,遗传算法迭代的多肋板型吸能构件具有较好的能量吸收参数,在平台阶段支撑反力的波动较小,能量吸收过程相对稳定,能有效达到能量吸收的效果。