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.

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).

Three-dimensional analysis of a thick FGM rectangular plate in thermal environment

The thermal behavior of a thick transversely isotropic FGM rectangular plate was investigated within the scope of three-dimensional elasticity. Noticing many FGMs may have temperature-dependent properties, the material constants were further considered as functions of temperature. A solution method based on state-space formulations with a laminate approximate model was proposed. For a thin plate, the method was clarified by comparison with the thin plate theory. The influences of material inhomogeneity and temperature-dependent characteristics were finally discussed through numerical examples.

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.

Hierarchical closed form solutions for plates bent by localized transverse loadings

3D and 2D closed form plate models are here applied to static analysis of simply supported square isotropic plates. 2D theories are hierarchically classified on the basis of the accuracy of the displacements and stresses obtained by comparison to the 3D exact results that could be assumed by the reader as benchmark for further analyses. Attention is mainly paid on localized loading conditions, that is, piecewise constant load. Also bi-sinusoidal and uniformly distributed loadings are taken into account. All of those configurations are considered in order to investigate the behavior of the 2D models in the case of continu- ous/uncontinuous, centric or off-centric loading conditions. The ratio between the side length a and the plate thickness h has been assumed as analysis parameter. Higher order 2D models yield accurate results for any considered load condition in the case of moderately thick plates, a/h=10. In the case of thick plates, a/h=5, and continuous/uncontinuous centric loading conditions high accuracy is also obtained. For the considered off-centric load condition and thick plates good results are provided for some output quantities. A better solution could be achieved by simply increasing the polynomial approximation order of the axiomatic 2D displacement field.

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.

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

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.

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].

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.

Factors affecting the dynamic response of pre-stressed anchors after transient excitation

The wide application of pre-stressed bolting technology in coal mine tunnels has made the nondestructive stress wave reflection method of determining bolting quality an important one. The effect of the support plate on the dynamic response of the pre-stressed anchor is of particular interest. A theoretical analysis and numerical simulations are used to identify the factors affecting the contact stress between the support plate and the rock wall. A formula allowing the calculation of contact stress is presented. Stress wave propagation through the nut, support plate, and rock wall are predicted. The dynamic response signals were measured in the field using prestressed anchors pre-tightened to different torques. The effects from the support plate on the dynamic response were recorded and the results compared to the predictions of pre-stressed anchor. This work provides a theoretical reference for the signal processing of dynamic reflected wave signals in anchor bolts.