应力圆与应变圆之间的关系

本文对各向同性弹性体，导出了用应变复数表示的应力圆方程，用该方程分析了应力圆与应变圆之间的关系，还用其对测得的应变分量直接进行平面应力状态的应力分析，计算简便．

用直角应变花测量某点应变的简便应变圆解法

通过理论推导，直接利用直角应变花的测量结果做出应变圆，并采用简单的方法解出主应变的大小和方向。

莫尔应变圆极点法及应变极点特性研究

极点是根据单元体的应变状态在莫尔应变圆上做出的一个特殊点,通过极点可以获得任意平面的应变状态。为确定莫尔应变圆上的极点,提出了2种方法——平行线法和法线法。采用反证法分别验证了平行线法和法线法确定的应变极点的唯一性,采用几何作图法分别验证了平行线法和法线法确定的应变极点的可靠性。研究表明:2种方法确定的应变极点位于莫尔应变圆的同一条直径上;应力极点与应变极点位于莫尔应力圆与应变圆组成的同心圆的半径上。莫尔应变圆极点法具有简便、准确的优点,避免了复杂的公式计算,是求解岩土工程中的稳定和变形问题及确定单元体复杂应变状态的优选方法。

有限应变测量的关键原理--摩尔圆

20世纪60年代,在板块理论建立的同时,对变形岩石和矿田构造作定量分析以替代定性分析的有限应变测量方法也建立了起来。定量分析的主要标志是将摩尔圆方法从力学引入到地质学,同时也引入矿田构造分析中,并且得到改进与发展。有限应变摩尔圆为分析岩石大变形而建立,极摩尔圆随后为分析广布于野外岩石中的一般剪切变形而建立。我国著名学者李四光在此之前将应力摩尔圆和库仑准则从力学领域介绍到构造地质学,尔后一些中国学者为改进和发展极摩尔圆方法作出了自己的贡献。本文以浅显的方式解释摩尔圆的基本概念和作图方法,附带做些练习和解答。

抛物面形零件冲压成形悬空侧壁圆锥台变形区的应力应变计算

应力和应变的分布情况可以反映出零件在成形过程中的变形特点,它是研究零件冲压成形的基础.采用主应力法推导出了冲压成形过程中旋转抛物面形零件悬空侧壁圆锥台变形区的应力和应变计算公式,以材料为SS304不锈钢的抛物面形零件为算例,得出其应力和应变分布趋势.另外,还计算出了抛物面形零件冲压成形时的应力分界圆直径和应变分界圆直径,其中,应变分界圆直径的计算结果与已有实验数据一致.通过对旋转抛物面形零件冲压成形过程中悬空侧壁圆锥台变形区应力和应变分布的研究,明确零件的成形过程和变形特点,为其冲压成形时内皱曲极限的预报与控制奠定了基础.

变形构造分析的定量化与摩尔圆的引用与发展

20世纪60年代,与板块构造学说建立的同时,在构造地质学中还有一项革新,就是变形构造分析的定量化,从定性描述走向定量计算。定量化的重要标志就是将力学中的摩尔圆引入构造地质学,并且使其改进和发展,在构造地质分析中建立了有限应变摩尔圆,适应了大变形的分析,又建立了极摩尔圆,适应一般剪切的分析。我国地质学家在其中也做出了自己的贡献。

球面零件拉深过程中三个特征圆的分析

分析了球面零件拉深中三个特征圆的关系、位置变化趋势及其影响因素并绘制相应曲线。

安全阀阀芯传感器的标定理论与验证技术

安全阀在线检测技术最重要的功能实现就是要解决大型生产装置运行周期不断延长,而安全泄放装置检验周期却有一年一检的严格限制之间的矛盾。安全阀是承压设备上的重要安全附件之一,作为生产装置安全的最后一道防线,本身具有很苛刻的性能要求,因此如何实现其在线检测,是生产装置实现长周期连续可靠运行的关健技术之一。为此,在专利技术指导下,设计研制了内嵌阀瓣膜传感器形式的新型安全阀。本文对安全阀中传感元件的布置、选择及标定技术原理等方面进行了理论和试验研究,结果表明这种带有阀芯薄膜传感器的新型安全阀运行稳定可靠,开启、回座迅速,密封性好,并且具有很好的检测灵敏度。

安全阀阀瓣膜传感器标定的理论与实验研究

通过对安全阀阀瓣膜传感器进行ANSYS数值模拟和相关实验研究,从理论和实验两方面探索了对阀瓣膜传感器进行标定问题,经过实验验证后,提出了一种准确可行的标定方案。首先,采用ANSYS软件模拟了阀瓣膜传感器承受不同载荷下的应变与压力的关系;同时也设计了一套阀瓣膜传感器的标定实验装置,利用该实验装置对阀瓣膜传感器进行了标定实验。标定实验结果分析表明,阀瓣在承受不同载荷的情况下,应变与压力呈良好的线性关系,线性度达到99.9%,并与相同载荷情况下ANSYS分析结果完全吻合,从而验证了这一标定实验方案的可靠性;通过对阀瓣膜传感器的灵敏度、线性度、重复性、滞后性等指标进行分析,结果显示其参数满足一般传感器的标准,验证了该传感器的可行性。

关于伤害

关于伤害廖华歌岁月漫漫，人的一生不可能不受到来自方方面面的一些伤害，只不过是受伤害的大小、轻重、深浅程度不同罢了。所谓伤害，就是使身体组织或思想感情受到损害。这种损害有来自自身的，有来自他人的；有主观的，有客观的；有故意的，有无意的。尽管性质不同，但...

Influences of strain softening and seepage on elastic and plastic solutions of circular openings in nonlinear rock masses

Considering the influence of strain softening, the solutions of stress, displacement, plastic softening region radius and plastic residual region radius were derived for circular openings in nonlinear rock masses subjected to seepage. The radial stress distribution curve, ground reaction curve, and relation curve between plastic softening region radius and supporting force in three different conditions were drawn respectively. From the comparisons among these results for different conditions, it is found that when the supporting force is the same, the displacement of tunnel wall considering both seepage and strain softening is 85.71% greater than that only considering seepage. The increase values of radial displacement at 0.95 m and plastic softening region radius at 6.6 m show that the seepage and strain softening have the most unfavorable effects on circular opening stability in strain softening rock masses.

On the Out-of-Plane Vibration of Rotating Circular Nanoplates

A rotating axisymmetric circular nanoplate is modeled by the Mindlin plate theory.The Mindlin plate theory incorporates the nonlocal scale and strain gradient effects.The shear deformation of the circular nanoplate is considered and the nonlocal strain gradient theory is utilized to derive the governing differential equation of motion that describes the out-of-plane free vibration behaviors of the nanoplate.The differential quadrature method is used to solve the governing equation numerically,and the natural frequencies of the out-of-plane vibration of rotating nanoplates are obtained accordingly.Two kinds of boundary conditions are commonly used in practical engineering,namely the fixed and simply supported constraints,and are considered in numerical examples.The variations of natural frequencies with respect to the thickness to radius ratio,the angular velocity,the nonlocal characteristic scale and the material characteristic scale are analyzed in detail.In particular,the critical angular velocity that measures whether the rotating circular nanoplate is stable or not is obtained numerically.The presented study has reference significance for the dynamic design and control of rotating circular nanostructures in current nano-technologies and nano-devices.

Experimental simulation investigation of influence of depth on spalling characteristics in circular hard rock tunnel

A series of true-triaxial compression tests were performed on red sandstone cubic specimens with a circular hole to investigate the influence of depth on induced spalling in tunnels.The failure process of the hole sidewalls was monitored and recorded in real-time by a micro-video monitoring equipment.The general failure evolution processes of the hole sidewall at different initial depths(500 m,1000 m and 1500 m)during the adjustment of vertical stress were obtained.The results show that the hole sidewall all formed spalling before resulting in strain rockburst,and ultimately forming a V-shaped notch.The far-field principal stress for the initial failure of the tunnel shows a good positive linear correlation with the depth.As the depth increases,the stress required for the initial failure of the tunnels clearly increased,the spalling became more intense;the size and mass of the rock fragments and depth and width of the V-shaped notches increased,and the range of the failure zone extends along the hole sidewall from the local area to the entire area.Therefore,as the depth increases,the support area around the tunnel should be increased accordingly to prevent spalling.

Dynamic cavitations in incompressible hyperelastic pre-strained circular sheets

A class of dynamic cavitations is examined for an isotropic incompressible hyperelastic circular sheet under a pre-strained state caused by an initially applied finite radial tension.The solutions that describe the radially symmetric motion of the pre-strained sheet are obtained.The conditions of cavitated bifurcation that describe cavity formation and motion with time at the axial line of the pre-strained sheet are proposed,that is to say,a circular cavity will form if the suddenly applied radial tensile load exceeds a certain critical value;dynamically,it is proved that the formed cavity will present a nonlinearly periodic oscillation,which is essentially different from the singular periodic oscillation of the formed cavity in an incompressible hyperelastic solid sphere.Numerical simulations show the effects of prescribed radial tension,material parameter and tensile load on critical ten-sile load describing cavity formation and periodic oscillation of the pre-strained circular sheet.

Vibration modes of flexoelectric circular plate

Beams,plates,and shells,as the fundamental mechanical structures,are widely used in microelectromechanical systems(MEMS)and nanoelectromechanical systems(NEMS)as sensors,actuators,energy harvesters,and among others.Deeply understand the electromechanical coupling of these dielectric structures is of crucial for designing,fabricating,and optimizing practice devices in these systems.Herein we demonstrate the electromechanical coupling in flexoelectric circular plate,in which higher-order strain gradients were considered to extend the classical electromechanical properties to isotropic materials,in which the non-uniform distribution of the electric potential along the radial direction was considered.Analytical solutions for the vibration modes of the flexoelectric circular plates showed that the dynamic modes were totally different from the piezoelectric circular plates owing to the inversion symmetry breaking by the strain gradient.The electromechanical coupling dynamic modes are sensitive to bending,twisting modes owing to the sensitivity of the flexoelectric effect to bending.This work provides a fundamental understanding of the electromechanical coupling in flexoelectric circular plate,which is helpful in designing novel flexoelectric circular plate-based devices,such as flexoelectric mirrors.

Axisymmetric 3:1 internal resonance of thin-walled hyperelastic cylindrical shells under both axial and radial excitations

Nonlinear vibration with axisymmetric 3:1 internal resonance is investigated for an incompressible neo-Hookean hyperelastic cylindrical shell under both axial and radial harmonic excitations.A full nonlinear strain-displacement relation is derived from the large deflection theory of thin-walled shells.A set of nonlinear differential equations describing the large deflection vibration are formulated by the Lagrange equation and the assumption of small strains.Steady-state responses of the system are predicted via the harmonic balance method with the arc length continuation,and their stabilities are determined via the modified sorting method.The effects of excitations on the steady-state responses are analyzed.The results reveal a crucial role played by the phase difference in the structural response,and the phase difference can effectively control the amplitude of vibration.

Gradient estimates for parabolic systems from composite material

In this paper, we derive W^(1,∞) and piecewise C^(1,α) estimates for solutions, and their t-derivatives, of divergence form parabolic systems with coefficients piecewise H¨older continuous in space variables x and smooth in t. This is an extension to parabolic systems of results of Li and Nirenberg [Comm Pure Appl Math, 2003, 56:892–925] on elliptic systems. These estimates depend on the shape and the size of the surfaces of discontinuity of the coefficients, but are independent of the distance between these surfaces.

Analysis of transient responses in a laminated piezoelectric cylindrical shell

A hybrid numerical method is proposed for analysis of transient responses in a multilayered piezoelectric cylindrical shell.In the present method,the associated equations of the displacement field and the electro-potential field are developed using an analytical-numerical method.The piezoelectric cylindrical shell is discretized into layered annular elements along the wall thickness direction.The governing equations are determined by Hamilton's Principle considering the coupling between the elastic and electric field in each element.The modal analysis and Fourier transformation with respect to the spatial cylindrical polar coordinates in the direction of wave propagation are introduced to formulate the displacement field and electro-potential field in the wave-number domain.The results of transient responses at any location can be obtained by performing an inverse Fourier transformation.The transient responses of an actual piezoelectric cylindrical shell excited by a coupled electro-mechanical circular line load are investigated as a numerical example.The computational results demonstrate the efficiency of the present method.