Modeling and Analysis of Vibration Characteristics of Rectangular Plate with Circular Through Hole Under Complex Boundary Conditions

This paper presents a method to study the free vibration of a plate with circular holes.The circular hole is regarded as a virtual small plate in which the mass density and Young's modulus are zero.Therefore,the free vibration problem of the circular hole plate can be transformed into the free vibration problem of the equivalent rectangular plate with non-uniform thickness.The model is derived from the spectral geometry method(SGM),and the displacement of the plate with circular holes is expanded by the modified Fourier series.Virtual springs are added to the boundary of the plate to simulate the boundary conditions of simply supported and fixed supports.The accuracy of this method is verified by comparison with the finite element calculation results.The relationship between modal numerical solutions of plates with circular holes and boundary conditions and geometry of the plate is studied.

Dynamic stress concentrations in thick plates with two holes based on refined theory

Based on complex variables and conformal mapping, the elastic wave scat- tering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem to be solved is changed to a set of infinite algebraic equations by an orthogonM function expansion method. As examples, under free boundary conditions, the numerical results of the dynamic moment concen- tration factors in the plates with two circular holes are computed. The results indicate that the parameters such as the incident wave number, the thickness of plates, and the spacing between holes have great effects on the dynamic stress distributions. The results are accurate because the refined equation is derived without any engineering hypothese.

Simple Proofs of Upper and Lower Envelopes of Van Der Pauw’s Equation for Hall-Plates with an Insulated Hole and Four Peripheral Point-Contacts

For plane singly-connected domains with insulating boundary and four point-sized contacts, C0 …C3, van der Pauw derived a famous equation relating the two trans-resistances R01,23, R12,30 with the sheet resistance without any other parameters. If the domain has one hole van der Pauw’s equation becomes an inequality with upper and lower bounds, the envelopes. This was conjectured by Szymański et al. in 2013, and only recently it was proven by Miyoshi et al. with elaborate mathematical tools. The present article gives new proofs closer to physical intuition and partly with simpler mathematics. It relies heavily on conformal transformation and it expresses for the first time the trans-resistances and the lower envelope in terms of Jacobi functions, elliptic integrals, and the modular lambda elliptic function. New simple formulae for the asymptotic limit of a very large hole are also given.

Three-Dimensional Stress Concentration Factor in Finite Width Plates with a Circular Hole

The three-dimensional stress concentration factor (SCF) at the edge of elliptical and circular holes in infinite plates under remote tension has been extensively investigated considering the variations of plate thickness, hole dimensions and material properties, such as the Poisson’s coefficient. This study employs three dimensional finite element modeling to numerically investigate the effect of plate width on the behavior of the SCF across the thickness of linear elastic isotropic plates with a through-the-thickness circular hole under remote tension. The problem is governed by two geometric non-dimensional parameters, i.e., the plate half-width to hole radius (W/r) and the plate thickness to hole radius (B/r) ratios. It is shown that for thin plates the value of the SCF is nearly constant throughout the thickness for any plate width. As the plate thickness increases, the point of maximum SCF shifts from the plate middle plane and approaches the free surface. When the ratio of plate half-width to hole radius (W/r) is greater than four, the maximum SCF was observed to approximate the theoretical value determined for infinite plates. When the plate width is reduced, the maximum SCF values significantly increase. A polynomial curve fitting was employed on the numerical results to generate empirical formulas for the maximum and surface SCFs as a function of W/r and B/r. These equations can be applied, with reasonable accuracy, to practical problems of structural strength and fatigue, for instance.

SINGULAR SOLUTIONS OF ANISOTROPIC PLATE WITH AN ELLIPTICAL HOLE OR A CRACK

In the present paper, closed form singular solutions for an infinite anisotropic plate with an elliptic hole or crack are derived based on the Stroh-type formalism for the general anisotropic plate. With the solutions, the hoop stresses and hoop moments around the elliptic hole as well as the stress intensity factors at the crack tip under concentrated in-plane stresses and bending moments are obtained. The singular solutions can be used for approximate analysis of an anisotropic plate weakened by a hole or a crack under concentrated forces and moments. They can also be used as fundamental solutions of boundary integral equations in BEM analysis for anisotropic plates with holes or cracks under general force and boundary conditions.

On a Problem of an Infinite Plate with a Curvilinear Hole inside the Unit Circle

In this work, we used the complex variable methods to derive the Goursat functions for the first and second fundamental problem of an infinite plate with a curvilinear hole C. The hole is mapped in the domain inside a unit circle by means of the rational mapping function. Many special cases are discussed and established of these functions. Also, many applications and examples are considered. The results indicate that the infinite plate with a curvilinear hole inside the unit circle is very pronounced.

A generalized plane strain theory for transversely isotropic piezoelectric plates

Study of generalized plane strain has so far been limited to elasticity. The present is aimed at parallel development of transversely isotropic piezoelasticity. By assuming that the along depth distribution of electric potential is linear, and that com- monly used Kane-Mindlin kinematical assumption is valid, two dimensional solution systems were deduced, for which, explicit solutions of the out-of-plane constraint factor, as well as the stress resultant concentration factor around a circular hole in a transversely isotropic piezoelectric plate subjected to remote biaxial tension are obtained. Comparisons of these formulas with their counterparts for elastic case yielded suggestions that whether the piezoelectric effect exacerbates or mitigates the stress resultant concentration greatly depends on material properties, particularly, the piezoelectric coefficients; the effect of plate thickness was extensively investigated.

The deformation and failure mechanism of cylindrical shell and square plate with pre-formed holes under blast loading

The deformation and failure mechanism of cylindrical shells and square plate with pre-formed holes under blast loading were investigated numerically by employing the Ansys 17.0 and Ls-Dyna 971.To calibrate the numerical model,the experiments of square plates with pre-formed circle holes were modeled and the numerical results have a good agreement with the experiment data.The calibrated numerical model was used to study the deformation and failure mechanism of cylindrical shells with pre-formed circle holes subjected to blast loading.The structure response and stress field changing process has been divided into four specific stages and the deformation mechanism has been discussed systematically.The local and global deformation curves,degree of damage,change of stress status and failure modes of cylindrical shell and square plate with pre-formed circular holes are obtained,compared and analyzed,it can be concluded as:(1)The transition of tensile stress fields is due to the geometrical characteristic of pre-formed holes and cylindrical shell with arch configuration;(2)The existence of preformed holes not only lead to the increasing of stress concentration around the holes,but also release the stress concentration during whole response process;(3)There are three and two kinds of failure modes for square plate and cylindrical shell with pre-formed holes,respectively.and the standoff distance has a key influence on the forming location of the crack initiating point and the locus of crack propagation;(4)The square plate with pre-formed holes has a better performance than cylindrical shell on blast-resistant capability at a smaller standoff distance,while the influence of pre-formed holes on the reduction of blast-resistant capability of square plate is bigger than that of cylindrical shell.

Three-Dimensional Scattering of an Incident Plane Shear Horizontal Guided Wave by a Partly through-Thickness Hole in a Plate

We investigate the three-dimensional （3D） scattering problem of an incident plane shear horizontal wave by a partly through-thickness hole in an isotropic plate, in which the Lamb wave modes are also included due to the mode conversions by the scattering obstacle in the 3D problem. An analytical model is presented such that the wave fields are expanded in all of propagating and evanescent SH modes and Lamb modes, and the scattered far-fields of three fundamental guided wave modes are analyzed numerically for different sizes of the holes and frequencies. The numerical results are verified by comparing with those obtained by using the approximate Poisson/Mindlin plate model for small hole radius and low frequency. It is also found that the scattering patterns are different from those of the SO wave incidence. Our work is useful for quantitative evaluation of the plate-like structure by ultrasonic guided waves.

Presence of Heat on an Infinite Plate with a Curvilinear Hole Having Two Poles

In the present paper Cauchy integral methods have been applied to derive exact and expressions for Goursat’s function for the first and second fundamental problems of isotropic homogeneous perforated infinite elastic media in the presence of uniform flow of heat. For this, we considered the problem of a thin infinite plate of specific thickness with a curvilinear hole where the origins lie in the hole is conformally mapped outside a unit circle by means of a specific rational mapping. Moreover, the three stress components σxx, σyy and σxy of the boundary value problem in the thermoelasticity plane are obtained. Many special cases of the conformal mapping and four applications for different cases are discussed and many main results are derived from the work.

STRESS INTENSITY FACTORS OF A PLATE WITH TWO CRACKS EMANATING FROM AN ARBITRARY HOLE

In this paper, Muskhelishvili complex function theory and boundary collocation method are used to calculate the stress intensity factors (SIF) of a plate with two cracks emanating from an arbitrary hole. The calculated examples include a circular, elliptical, rectangular, or rhombic hole in a plate. The principle and procedure by the method is not only rather simple, but also has good accuracy. The SIF values calculated compare very favorably with the existing solutions. A t the same time,the method can be used far different finite plate with two cracks emanating from a hole with more complex geometrical and loading conditions. It is an effective unified approach for this kind of fracture problems.

Using Refined Theory to Studied Elastic Wave Scattering and Dynamic Stress Concentrations in Plates with Two Cutouts

In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. According to free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with two circular cutouts analyze that: there will be more complex interaction changes between two-cutout situation than single cutout situation. In the case of low frequency or high frequency and thin plate, the hole-spacing in the absence of coupling interactions was larger or smaller. The numerical results and method can be used to analyze the dynamics and strength of plate-like structures.

后路单开门钉板固定结合Key-hole技术在混合型颈椎病患者中的应用效果

目的:分析后路单开门钉板固定结合Key-hole技术在混合型颈椎病患者中的应用效果。方法:采用前瞻性分析法,以随机数表法将2021年6月至2023年6月濮阳市人民医院120例混合型颈椎病患者分为对照组和观察组,各60例。对照组患者采用后路单开门钉板固定治疗,观察组患者采用后路单开门钉板固定结合Key-hole技术治疗。对两组患者术前和术后3个月的JOA评分、JOA评分改善率、Cobb角、ROM、颈椎肌张力及术后3个月的并发症情况进行比较。结果:与对照组相比,术后观察组的JOA评分、JOA评分改善率均升高,术后观察组的Cobb角、ROM、颈椎肌张力均升高,术后3个月观察组的神经根症状总有效率升高,术后3个月内观察组的并发症总发生率降低,差异有统计学意义(P<0.05)。结论:后路单开门钉板固定结合Key-hole技术能够有效缓解混合型颈椎病患者的颈髓、神经根压迫,改善颈髓、神经根功能,且可减少并发症发生。

Computational Complex Method for Finite Elastic Plane Problem with Multiple Elliptical Holes

把多复变量应力函数和边界配点最小二乘法相结合，计算含有任意多个椭圆孔有限大小弹性板的应力场．每个孔的大小、位置为任意．板的边界由下列四种边界条件以及它们的组合所组成：１）已知Ｐｘ和Ｐｙ的应力边界，２）已知Ｖｘ和Ｖｙ的位移边界，３）已知法向位移ＶＮ和切向力ＰＴ的混合边界，４）已知法向力ＰＮ和切向位移ＶＴ的混合边界．编制了相应的ＦＯＲＴＲＡＮ程序，进行考题和算例分析，结果表明本方法行之有效．

Study on the mechanism of near-field underwater explosion on supported thin plates with prefabricated holes

In this study,underwater explosion tests with 2.5 g trinitrotoluene explosive under different fixed plates with prefabricated holes were conducted.The experimental results showed that the air inflow from the prefabricated hole caused the bubble to collapse earlier with an increase in the hole diameter.In addition,the deformation mode of the thin plate transitioned from“convex”to“concave”(up to down).Next,the coupled Eulerian-Lagrangian method was used to perform the corresponding numerical simulation.The accuracy of the numerical simulation method was verified through a comparison with the experimental data.In addition,a series of numerical simulations were conducted with different prefabricated-hole diameters,blast distances,and prefabricated-hole shapes.The results showed that the bubble-pulsating water jet substantially influenced the deformation of the thin plate when the diameter of the prefabricated hole was within the theoretical maximum bubble radius.When the blast distance was within the theoretical maximum bubble radius,the thin plate was subjected to only a single bubble pulsation owing to the air inflow from the prefabricated hole.

CALCULATION OF STRESSES IN A MULTIPLY-CONNECTED ANISOTROPIC PLATE USING STRESS FUNCTIONS OF MULTIPLE COMPLEX VARIABLES

On the basis of anisotropic mathematical elasticity,using multiple conformal representations, the stress functions of multiple complex variables for an infinite multiply-connected anisotropic plate are de- rived.The functions are developed in Fourier series on unit circles,and the unknown coefficients of the functions are determined by undetermined coefficients method.Then the stresses in the plate can be calcu- lated.A plate containing multiple elliptical holes or cracks is discussed,and the corresponding FORTRAN77 program is developed.Five examples are given.The results show that this method is very effective and convenient.

Stress concentration coefficients of optimized cope-hole welded detail

The fatigue performance of optimized welded detail has been investigated by fatigue experiments of three welded specimens under different loadings.In addition,local finite element models of this welded detail were established using finite element software ANSYS.The influences of different factors such as plate thickness,plate gap and initial geometric imperfections on the stress concentration coefficient(SCC) were discussed.The experimental results indicate that the fatigue life of three specimens for this welded detail is 736,000,1,044,200 and 1,920,300 times,respectively.The web thickness,the filler plate thickness and the initial geometric imperfection have relatively less effect on the SCCs of this welded detail.However,cope-hole radius is influential on the SCCs of the web and the weld.The SCC of weld is significantly affected by the weld size and plate gap,but the SCCs of other parts of the welded detail are hardly affected by the plate gap.

A New Two Way Stop Plate in Loom Equipment

This design offer the two way stop used plate on warp. It is applicable to textile equipment, especially for loom equipment. The characteristics are that there are two similar long grooves in the different sides of the yarn hole, so that it can be used in two way and the life cycle is twice as long as that of the present one.

沿空留巷密集钻孔切顶机理及关键参数确定方法

为实现密集钻孔切顶条件下沿空留巷顶板结构安全稳定,研究正常情况与密集钻孔条件下顶板岩层结构受力状况,基于岩石断裂理论和弹性理论分析回采前后顶板密集钻孔孔间围岩受力分布及其破断过程,明确密集钻孔切顶机理及相邻钻孔的孔间集中应力相互作用机制,推导工作面端头弧形三角板结构巷道侧边界密集钻孔孔间围岩的拉剪应力计算公式。在此基础上,分析不同参数对孔间围岩所受拉剪应力的影响作用,提出沿空留巷密集钻孔切顶关键参数确定方法。研究表明:密集钻孔主要通过回采前后钻孔周围应力条件改变来增加钻孔围岩拉剪应力集中程度,引起孔间裂隙扩张联通,形成切缝线破断关键岩层。回采前钻孔主要受水平挤压应力影响,回采后钻孔受力逐渐转变为采空区顶板回转下沉产生的拉剪应力为主,钻孔孔间围岩状态随之由孔间围岩弱化阶段过渡到孔壁裂纹成形阶段,再转变为孔间围岩破断阶段。密集钻孔孔间围岩所受拉剪应力大小主要取决于关键岩层厚度及钻孔孔径与孔间距之比,与钻孔高度及间距成负相关,与角度及直径正相关。据此提出了密集钻孔关键参数确定方法,并根据龙滩矿3124 N工作面坚硬顶板条件设计了密集钻孔切顶留巷方案,确定钻孔长度为8.3 m,角度为15°,钻孔直径为48 mm,间距为500 mm。留巷后巷道顶帮变形可控且整体稳定性较好,由此可证明密集钻孔布置参数较为合理,密集钻孔关键参数确定方法有效可行。

高寒区隧道洞口段覆雪波纹钢棚洞减载方法研究

高寒区隧道洞口段易受上方覆雪及落石影响,采用现有大跨径波纹钢棚洞会产生较大变形和失稳,影响边疆公路运行安全。为此,依托某线路隧道洞口段波纹钢防雪棚洞项目,从拱效应及加筋桥减载原理出发,运用有限元软件构建了EPS板、EPS板+加筋雪、EPS板+加筋冰等10种减载方案的三维波纹钢棚洞模型,研究不同减载方案对棚洞应力、棚洞变形和覆雪压力的影响,对比分析棚洞受力变形特征及减载效果,筛选出最优减载方案。结果表明:施加减载材料后,棚洞上方覆雪压力均不同程度分散到棚洞两侧,减小了棚洞结构的受力;随着覆雪高度增加,减载效果更显著,其中30 cmEPS板+加筋冰组合式方案的减载效果最佳,棚顶应力减少32.72%,棚顶位移减小22.63%;针对波纹钢棚洞的减载问题,建议隧道洞口30 m范围内采用30 cmEPS板+加筋雪方案,距隧道口30 m以外范围可采用30 cmEPS板+加筋冰方案。