Static and dynamic snap-through behaviour of an elastic spherical shell

The deformation and snap-through behaviour of athin-walled elastic spherical shell statically compressed on aflat surface or impacted against a flat surface are studied theoretically and numerically in order to estimate the influenceof the dynamic effects on the response.A table tennis ballis considered as an example of a thin-walled elastic shell.Itis shown that the increase of the impact velocity leads to avariation of the deformed shape thus resulting in larger deformation energy.The increase of the contact force is causedby both the increased contribution of the inertia forces andcontribution of the increased deformation energy.The contact force resulted from deformation/inertia ofthe ball and the shape of the deformed region are calculated by the proposed theoretical models and compared withthe results from both the finite element analysis and somepreviously obtained experimental data.Good agreement isdemonstrated.     

Variational analysis of gradient elastic flexural plates under static loading

Gradient elastic flexural Kirchhoff plates under static loading are considered. Their governing equation of equilibrium in terms of their lateral deflection is a sixth order partial differential equation instead of the fourth order one for the classical case. A variational formulation of the problem is established with the aid of the principle of virtual work and used to determine all possible boundary conditions, classical and non-classical ones. Two circular gradient elastic plates, clamped or simply supported at their boundaries, are analyzed analytically and the gradient effect on their static response is assessed in detail. A rectangular gradient elastic plate, simply supported at its boundaries, is also analyzed analytically and its rationally obtained boundary conditions are compared with the heuristically obtained ones in a previous publication of the authors. Finally, a plate with two opposite sides clamped experiencing cylindrical bending is also analyzed and its response compared against that for the cases of micropolar and couple-stress elasticity theories.     

A FURTHER STUDY OF THE THEORY OF ELASTIC CIRCULAR PLATES WITH NON－KIRCHHOFF－LOVE ASSUMPTIONS

ＡＦＵＲＴＨＥＲＳＴＵＤＹＯＦＴＨＥＴＨＥＯＲＹＯＦＥＬＡＳＴＩＣＣＩＲＣＵＬＡＲＰＬＡＴＥＳＷＩＴＨＮＯＮ－ＫＩＲＣＨＨＯＦＦ－ＬＯＶＥＡＳＳＵＭＰＴＩＯＮＳＣｈｉｅｎＷｅｉ－ｚａｎｇ（钱伟长）ＲｕＸｕｅ－ｐｉｎｇ（茹学萍）（ＳｈａｎｇｈａｉＵｎｉ...     

Size effects on strength, toughness and fatigue crack growth of gradient elastic solids

The present study investigates the microstructural size effect on the strength of a bar under axial loading, and on the toughness and crack growth of a beam under three-point bending within the framework of strain gradient elasticity. The gradient responses have been found considerably tougher as compared to the classical theory predictions and the observed deviation increases with increasing values of the non-dimensional parameter g/L (microstructural length over structural length). Based on the analytical solution of the strain energy release rate for the three-point bending case, a new, simple and universal, strain gradient elasticity, brittle fracture criterion and a new, size adjusted fatigue crack growth law have been established. Finally, the analytical predictions of the current modeling compare well with previous experimental data, based on three-point bending tests on single-edge notched concrete beams.     

Theory of nonlinear dynamic stability for composite laminated plates

In this paper,the general equations of dynamic stability for composite laminatedplates are derived by Hamilton principle.These general equations can be used to considerthose different factors that affect the dynamic stability of laminated plates.The factors aretransverse shear deformation,initial imperfections,longitudinal and rotational inertia,andply-angle of the fiber,etc.The solutions of the fundamental equations show that someimportant characteristics of the dynamic instability can only be got by the considerationand analysis of those factors     

Large deflection analysis of the moderately thick general theta ply laminated plates on nonlinear elastic foundation with various boundary conditions

This paper presents a powerful method i.e. the kinetic Dynamic Relaxation for analyzing general theta ply laminated plates, resting on nonlinear elastic foundation with different boundary conditions. Comprehensive comparison and parametric studies prove accuracy and efficiency of the proposed approach with interesting specifications such as fully vector calculations, independency to configuration, situation and angle of plies so that general theta ply laminated plate with simultaneous coupling between membrane, bending and shear strains could be analyzed as simple as analyzing of symmetric cross ply plate. Moreover, the proposed technique could simply satisfy complicated boundary conditions such as free and movable edges.     

Reflection and transmission of elastic waves at five types of possible interfaces between two dipolar gradient elastic half-spaces

Reflection and transmission of an incident plane wave at five types of possible interfaces between two dipo-lar gradient elastic solids are studied in this paper. First, the explicit expressions of monopolar tractions and dipolar trac-tions are derived from the postulated function of strain energy density. Then, the displacements, the normal derivative of displacements, monopolar tractions, and dipolar tractions are used to create the nontraditional interface conditions. There are five types of possible interfaces based on all possible combinations of the displacements and the normal derivative of displacements. These interfacial conditions with consid-eration of microstructure effects are used to determine the amplitude ratio of the reflection and transmission waves with respect to the incident wave. Further, the energy ratios of the reflection and transmission waves with respect to the incident wave are calculated. Some numerical results of the reflection and transmission coefficients are given in terms of energy flux ratio for five types of possible interfaces. The influences of the five types of possible interfaces on the energy parti-tion between the refection waves and the transmission waves are discussed, and the concept of double channels of energy transfer is first proposed to explain the different influences of five types of interfaces.     

Nonlinear analysis of skewed sandwich plates

Nonlinear static and dynamic behaviours of freely supported Rhombic sandwich plates have been studied following Banerjee's hypothesis. Numerical results for 0° skew angle are compared with other known results. Results for other skew angles are believed to be new.

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Sommario Si studia, seguendo l'ipotesi di Banerjee, il comportamento nonlineare statico e dinamico di piastre rombiche semplicemente appoggiate. Si presentano risultati numerici relativi a piastre rombiche e rettangolari: questi ultimi vengono paragonati a risultati già noti, mentre i primi si ritengono nuovi.

     

Measurements of dynamic properties of concrete structures using flexural wave propagation characteristics

Flexural wave propagation characteristics influence the impact noise generation of concrete structures that are found in building floors, railroads, bridges, and many other engineering structures. The flexural vibration of the structure is affected by concrete dynamic properties. The purpose of this study is to measure the concrete dynamic characteristics using a wave propagation approach. The flexural wave speeds, bending stiffness and their loss factors were measured. The measured characteristics are essential for understanding sound radiation and vibration dissipation capabilities of the concrete structures. Various concrete beam structures were made and tested. The dynamic stiffness and loss factor were influenced by its components and showed frequency-dependent variation, especially for the measured loss factor.     

Non-linear theories of beams and plates accounting for moderate rotations and material length scales

The primary objective of this paper is to formulate the governing equations of shear deformable beams and plates that account for moderate rotations and microstructural material length scales. This is done using two different approaches: (1) a modified von Kármán non-linear theory with modified couple stress model and (2) a gradient elasticity theory of fully constrained finitely deforming hyperelastic cosserat continuum where the directors are constrained to rotate with the body rotation. Such theories would be useful in determining the response of elastic continua, for example, consisting of embedded stiff short fibers or inclusions and that accounts for certain longer range interactions. Unlike a conventional approach based on postulating additional balance laws or ad hoc addition of terms to the strain energy functional, the approaches presented here extend existing ideas to thermodynamically consistent models. Two major ideas introduced are: (1) inclusion of the same order terms in the strain–displacement relations as those in the conventional von Kármán non-linear strains and (2) the use of the polar decomposition theorem as a constraint and a representation for finite rotations in terms of displacement gradients for large deformation beam and plate theories. Classical couple stress theory is recovered for small strains from the ideas expressed in (1) and (2). As a part of this development, an overview of Eringen׳s non-local, Mindlin׳s modified couple stress theory, and the gradient elasticity theory of Srinivasa–Reddy is presented.     

Bending and stability analysis of gradient elastic beams

The problems of bending and stability of Bernoulli–Euler beams are solved analytically on the basis of a simple linear theory of gradient elasticity with surface energy. The governing equations of equilibrium are obtained by both a combination of the basic equations and a variational statement. The additional boundary conditions are obtained by both variational and weighted residual approaches. Two boundary value problems (one for bending and one for stability) are solved and the gradient elasticity effect on the beam bending response and its critical (buckling) load is assessed for both cases. It is found that beam deflections decrease and buckling load increases for increasing values of the gradient coefficient, while the surface energy effect is small and insignificant for bending and buckling, respectively.     

基于边光滑有限元法的加筋板静力和自由振动分析

运用边光滑有限元法,研究分析了加筋板结构的静力和自由振动问题。在边光滑有限元法中,将基于边的应变光滑技术用于对原来的应变场进行光滑操作;由于应变光滑技术能够适当地软化原来过刚的有限元模型,从而能够得到更加接近于系统准确刚度的光滑有限元模型;鉴于三角形单元良好的适用性,选用三角形单元对模型进行网格划分;同时,为了解决低阶Reissner-Mindlin板单元弯曲过程中的横向剪切自锁问题,采用了一种新型的离散剪切间隙技术。算例的数值计算结果表明,与传统的有限元法相比,边光滑有限元法能够得到精度更高的计算结果,且收敛更快,计算效率更佳。     

具有弹性支座杆件的动力稳定性研究

研究了杆件具有弹性支座时直杆的动力稳定性问题，推导出了杆件的临界频率和动力不稳定边界，分析了弹簧刚度和阻尼对杆件动力稳定性的影响，研究表明杆件的侧向刚度愈大其结构的动力稳定性愈好，阻尼对杆的振动起有利作用，并提出了在实际工程中减小杆件振动的一些措施．     

The bending,stability and vibrations of rectangular plates with free edges on elastic foundations

This paper discusses the problems of the bending, stability and vibrations of the rectangular plates with free boundaries on elastic foundations. In the present paper we select a flexural function, which satisfies not only all the boundary conditions of free edges but also the conditions at free corner points, and consequently we obtain a better approximate solution. The energy method is used in this paper.     

A Combined Static/Dynamic Technique for Damage Detection of Laminated Composite Plates

There is a growing demand to develop viable techniques for effective damage detection of composite structures, and the dynamics-based approach has been broadly used in structural health monitoring. A new combined static/dynamic technique for improved damage detection of laminated composite plates is presented. The promise of the technique is that under the sustaining static load, the abnormality of dynamic response due to damage may become more pronounced and easy to be detected. The experimental program consists of testing an E-glass/epoxy composite plate with an embedded delamination under a pre-set static compressive force, and the dynamic response of laminated composite plates is measured using two different actuator–sensor systems: (1) PZT (lead–zirconate–titanate) actuators and scanning laser vibrometer (SLV) sensing system (PZT–SLV), and (2) PZT actuators and Polyvinylidenefluoride (PVDF) sensors (PZT–PVDF). The influence of sustaining static forces to dynamic response of delaminated composite plates is evaluated. The numerical finite element (FE) analysis is also conducted to verify the effectiveness of this technique. The experimental and numerical mode shapes are used to detect the presence, location, and size of the delamination and to study the effect of static load on dynamic response. Two relatively new damage detection algorithms (i.e., Simplified Gapped Smoothing Method (GSM) and Generalized Fractal Dimension (GFD)) are employed to analyze the Uniform Load Surface (ULS) calculated from the experimental and numerical data. From the dynamic response and analysis results using the damage detection algorithms, it is observed that as the sustaining static load increases, the delamination is much easier to be identified through the enlarged damage parameters. The present combined static/dynamic technique is capable of magnifying the effect of damage, thus improving the effectiveness of damage detection.     

A structural gradient theory of torsion,the effects of pretwist,and the tension of pre-twisted DNA

A structural gradient theory of torsion of thin-walled beams is developed. A non-local estimate of the mean value of the angle of twist of the beam leads to a shear gradient that is energetically consistent with a bi-moment, in the spirit of the averaging theory of Vardoulakis and Giannakopoulos (2006). The geometric details of the cross section play the role of the microstructure of the beam, introducing a size effect in the torsion problem. The appropriate boundary conditions are derived from the variational formulation of the problem. The proposed gradient elasticity theory is identical to Vlasov’s torsion theory of thin walled elastic beams. The tension of pre-twisted DNA is analyzed at high axial loads, where enthalpic elasticity prevails. A size effect is naturally introduced, indicating that shorter DNA lengths lead to stiffer response in torsion. It is shown also that the complete unwinding of DNA triggers the debonding of its strands.     

基于小波微分求积法的薄板弯曲分析

利用小波微分求积法(WDQM)对任意荷载作用下的薄板弯曲问题进行了求解分析。数值算例表明,小波微分求积法与一般的DQ法相比具有很好的适用性,特别是薄板受集中荷载或不连续分布荷载作用时,由于小波基函数的紧支撑特性与其对突变信号良好的描述能力,WDQ法的精度明显优于一般的DQ法,具有良好的应用前景。     

Torsional vibrations of a column of fine-grained material: A gradient elastic approach

The gradient theory of elasticity with damping is successfully employed to explain the experimentally observed shift in resonance frequencies during forced harmonic torsional vibration tests of columns made of fine-grained material from their theoretically computed values on the basis of the classical theory of elasticity with damping. To this end, the governing equation of torsional vibrations of a column with circular cross-section is derived both by the lattice theory and the continuum gradient elasticity theory with damping, with consideration of micro-stiffness and micro-inertia effects. Both cases of a column with two rotating masses attached at its top and bottom, and of a column fixed at its base carrying a rotating mass at its free top, are considered. The presence of both micro-stiffness and micro-inertia effects helps to explain the observed natural frequency shift to the left or to the right of the classical values depending on the nature of interparticle forces (repulsive or attractive) due to particle charge. A method for using resonance column tests to determine not only the shear modulus but also the micro-stiffness and micro-inertia coefficients of gradient elasticity for fine-grained materials is proposed.     

The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models

We consider a wide class of gradient damage models which are characterized by two constitutive functions after a normalization of the scalar damage parameter. The evolution problem is formulated following a variational approach based on the principles of irreversibility, stability and energy balance. Applied to a monotonically increasing traction test of a one-dimensional bar, we consider the homogeneous response where both the strain and the damage fields are uniform in space. In the case of a softening behavior, we show that the homogeneous state of the bar at a given time is stable provided that the length of the bar is less than a state dependent critical value and unstable otherwise. However, we also show that bifurcations can appear even if the homogeneous state is stable. All these results are obtained in a closed form. Finally, we propose a practical method to identify the two constitutive functions. This method is based on the measure of the homogeneous response in a situation where this response is stable without possibility of bifurcation, and on a procedure which gives the opportunity to detect its loss of stability. All the theoretical analyses are illustrated by examples.     

An exact symplectic solution for the dynamic analysis of shear deformable antisymmetric angle-ply laminated plates

From the mixed variational principle, by the selection of the state variables and its dual variables, the Hamiltonian canonical equation for the dynamic analysis of shear deformable antisymmetric angle-ply laminated plates is derived, leading to the mathematical frame of symplectic geometry and algorithms, and the exact solution for the arbitrary boundary conditions is also derived by the adjoint orthonormalized symplectic expansion method. Numerical results are presented with the emphasis on the effects of length/thickness ratio, arbitrary boundary conditions, degrees of anisotropy, number of layers, ply-angles and the corrected coefficients of transverse shear.