Dynamic-finite-element and dynamic-photoelastic analyses of two fracturing homalite-100 plates

A dynamic-finite-element code, HONDO, was used to analyze two single-edged-notch fracturing Homalite-100 plates which had been previously studied by dynamic photoelasticity. A single-edged crack in the finite-element model was advanced in incremental jumps such that the time-averaged crack velocity matched the measured crack velocity in the Homalite-100 plate. Dynamic-energy-release rates were computed for a constant-velocity crack and a crack which arrested after a somewhat constant deceleration. These results were compared with the corresponding dynamic-energy-release rates, which were computed from the dynamic-stress-intensity factors determined by dynamic photoelasticity, and with static-strain energyrelease rates. Despite the crude modeling of the running crack, the coarseness of the finite-element-grid breakdown and the differences in the modeled and actual grip conditions, the computed and measured dynamic-energy-release rates, except for occasional large differences, generally agreed within 10 percent of each other.     

Perforation of steel and polycarbonate plates by tumbling projectiles

An experimental investigation to assess the effect of tumbling by hard-steel, blunt-faced cylindrical projectiles on the impact response of thin 4130 steel and polycarbonate target plates was performed. Deformation and failure phenomena were observed and discussed; comparisons of the results with analytical models and numerical stimulation, described in a previous paper, were also performed for the steel targets. The final velocity of the projectile and the crater length in the target were correlated with the striker impact angle (or yaw angle with a zero oblique angle); reasonable agreement was attained among the experimental, analytical and numerical results. It was found that an increase of the impact angle can increase the velocity drop and the crater length markedly. The increase tends to be stabilized after the impact angle exceeds 50° and the consequences in such a case are almost the same as in side-on impact.     

A semi-analytical solution for static and dynamic analysis of plates with piezoelectric patches

A modified mixed variational principle for piezoelectric materials is established and the state-vector equation of piezoelectric plates is deduced directly from the principle. Then the exact solution of the state-vector equation is simply given, and based on the semi-analytical solution of the state-vector equation, a realistic mathematical model is proposed for static analysis of a hybrid laminate and dynamic analysis of a clamped aluminum plate with piezoelectric patches. Both the plate and patches are considered as two three-dimensional piezoelectric bodies, but the same linear quadrilateral element is used to discretize the plate and patches. This method accounts for the compatibility of generalized displacements and generalized stresses on the interface between the plate and patches, and the transverse shear deformation and the rotary inertia of the plate and patches are also considered in the global algebraic equation system. Meanwhile, there is no restriction on the thickness of plate and patches. The model can be also modified to achieve a semi-analytical solution for the transient responses to dynamic loadings and the vibration control of laminated plate with piezoelectric patches or piezoelectric stiffeners.     

Modeling and analysis of micro-sized plates resting on elastic medium using the modified couple stress theory

Analytical solutions for bending, buckling, and vibration of micro-sized plates on elastic medium using the modified couple stress theory are presented. The governing equations for bending, buckling and vibration are obtained via Hamilton’s principles in conjunctions with the modified couple stress and Kirchhoff plate theories. The surrounding elastic medium is modeled as the Winkler elastic foundation. Navier’s method is being employed and analytical solutions for the bending, buckling and free vibration problems are obtained. Influences of the elastic medium and the length scale parameter on the bending, buckling, and vibration properties are discussed.     

Nonlinear dynamic analysis of circular plates with varying thickness

The BEM is developed for nonlinear free and forced vibrations of circular plates with variable thickness undergoing large deflections. General boundary conditions are considered, which may be also nonlinear. The problem is formulated in terms of displacements. The solution is based on the concept of the analog equation, according to which the two coupled nonlinear differential equations with variable coefficients pertaining to the in-plane radial and transverse deformation are converted to two uncoupled linear ones of a substitute beam with unit axial and unit bending stiffness, respectively, under fictitious quasi-static load distributions. Numerical examples are presented which illustrate the method and demonstrate its accuracy.     

A novel dynamic friction experiment using a modified kolsky bar apparatus

A novel dynamic friction experiment using the Kolsky bar concept was developed. The technique is complementary to the plate impact and other macroscopic friction experiments in the sense that sliding velocities and pressures not attainable otherwise can be investigated. The experimental results reported in this article show that the technique provides accurate and repeatable measurement of time-resolved friction. The apparatus is simpler and easier to operate than the plate impact facility. However, it cannot achieve the same level of contact pressure. Several material pairs have been investigated. In particular, the kinetic friction coefficient of Ti-6Al-4V sliding against WC/Co (cermet) and 4340 steel sliding against WC/Co were measured and compared with the values reported by Prakash and Clifton in 1993. Atomic force microscopy is used to characterize the surface topography before and after the friction tests.     

Photoelastic analysis of frozen stressed specimens using spectral-contents analysis

The complete birefringence, or isochromatic fringe order, in stress-frozen photoelastic models has been found by measuring the spectral contents of idividual points. A calibration procedure is porposed. The effects of nonuniform birefringence and dispersion of birefringence are considered. The results are presented from the analysis of models of a plate with a central hole and a disk subject to three radial loads.     

Large deflection static and dynamic analysis of isotropic and orthotropic annular plates

In the present paper, Chebyshev series are employed to obtain the non-linear static and dynamic response of isotropic and orthotropic annular plates. The non-linear partial differential equations obtained from von Karman's large deflection plate theory have been solved by using the Chebyshev series in the space domain and the Houbolt numerical integration scheme in the time domain. Two different sets of boundary conditions of the annulus are investigated and detailed numerical results have been obtained for different cases of orthotropy and geometry.     

复合材料层合板壳的非线性热动态响应分析

本文基于高阶剪切变形理论，考虑同天应变和横向剪切应变的影响，对受热复合材料层合板壳的非线性热动态响应进行分析，计及了转动惯量的影响，给出了通用性较好的Ｃ＾０类有限元公式，文中数值算同现有文献和三维有限元计算结果进行了比较，证明了本文方法的精确、有效性，文中还就层合板的边界条件、纵厚比及铺设角度对非线性热动态响应的影响进行了分析。     

Two-mode Galerkin approach in dynamic stability analysis of viscoelastic plates

ＩｎｔｒｏｄｕｃｔｉｏｎＤｙｎａｍｉｃｓｔａｂｉｌｉｔｙａｎａｌｙｓｉｓｏｆｖｉｓｃｏｅｌａｓｔｉｃｓｔｒｕｃｔｕｒｅｓｉｓｍｕｃｈｍｏｒｅｃｏｍｐｌｉｃａｔｅｄｓｉｎｃｅｔｈｅｍａｔｈｅｍａｔｉｃａｌｍｏｄｅｌｔｕｒｎｓｏｕｔｔｏｂｅａｓｙｓｔｅｍｏｆｉｎｔｅｇｒｏ＿ｐａｒｔｉａｌ＿ｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ,ｒａｔｈｅｒｔｈａｎａｓｙｓｔｅｍｏｆｐａｒｔｉａｌｄｉｆｆｅｒｅｎｔｉａｌｏｎｅｓａｓｉｎｔｈｅｅｌａｓｔｉｃｓｔｒｕｃｔｕｒｅ[1].Ｍａｎｙｗｏｒｋｓｈａｖｅｂｅｅｎｐ…     

A modified upper bound approach to limit analysis for plane strain deeply cracked specimens

The classical upper bound approach of limit analysis is based on assumption of rigid blocks of deformation that move between lines of tangential displacement discontinuity. This assumption leads to considerable simplification but often at cost of higher estimate of the actual load. Moreover, in many cases, it does not give a correct shape of the plastic field. In order to overcome these limitations a modified upper bound approach is proposed in this article. The proposed approach is basically an energetic approach but unlike the classical upper bound approach it is capable of including presence of statically governed stress field. As an application, of proposed approach, theoretical plane strain solutions are presented for deeply cracked fracture mechanics specimens (single edge cracked specimen in pure bending – SE (PB), single edge cracked specimen in three-point bending – SE (B), and compact tension – C (T) specimens). Plane strain plasticity problem in rigid elastic–plastic mono-material (homogeneous) was solved to evaluate useful parameters like limit load, plastic eta function (η_p) and plastic rotation factor (r_p) and in bi-material (mismatch welds) to evaluate mismatch limit load, for deeply cracked specimens. New kinematically admissible velocity fields are proposed for SE (B) and C (T) specimens. Proposed theoretical solutions were confirmed by classical slip-line field solutions, wherever available, and by detailed elastic–plastic finite element analysis with Von-Mises yield criterion. Good agreement was found between proposed solutions and results obtained from the classical slip-line field theory and finite element analysis.     

Static, stability and dynamic analysis of gradient elastic flexural Kirchhoff plates

The governing equation of motion of gradient elastic flexural Kirchhoff plates, including the effect of in-plane constant forces on bending, is explicitly derived. This is accomplished by appropriately combining the equations of flexural motion in terms of moments, shear and in-plane forces, the moment–stress relations and the stress–strain equations of a simple strain gradient elastic theory with just one constant (the internal length squared), in addition to the two classical elastic moduli. The resulting partial differential equation in terms of the lateral deflection of the plate is of the sixth order instead of the fourth, which is the case for the classical elastic case. Three boundary value problems dealing with static, stability and dynamic analysis of a rectangular simply supported all-around gradient elastic flexural plate are solved analytically. Non-classical boundary conditions, in additional to the classical ones, have to be utilized. An assessment of the effect of the gradient coefficient on the static or dynamic response of the plate, its buckling load and natural frequencies is also made by comparing the gradient type of solutions against the classical ones.     

The size of plastic zones in cracked plates made of polycarbonate

The influence of the thickness of a cracked plate, made of Polycarbonate of Bisphenol A, on the plastic zones developed at the crack tip was studied. The three-dimensional character of yielding at the vicinity of the crack tip is revealed. The study of the thickness variation in the plastic zones is made by applying the shadow-moiré method. It has been derived that the thickness variation in the plastic zones is discontinuous with successive dimples of different thickness. The influence of the overall thickness of the specimen on the size and length of the plastic zone was studied for different crack lengths. Irwin's theory for small yielding, as well as the simple and modified Dugdale-Barenblatt models, were applied for the study of plastic zones. By comparing the plastic-zone lengths in relation to their shape, with those given by the above theories, it may be concluded that, for small loads where the applied stress σ is not exceeding 0.40 of the yield stress \(\sigma _o \) in tension and small values of the ratio of crack lengtha to plate thicknesst, (a/t<4) a state of plane strain dominates at the vicinity of the crack tip, while, by increasing the load and ratioa/t, the plastic zones approach in shape and size those given by the modified Dugdale-Barenblatt model.     

Nonlinear dynamic analysis of moving bilayer plates resting on elastic foundations

The aim of this study is to investigate the dynamic response of axially moving two-layer laminated plates on the Winkler and Pasternak foundations. The upper and lower layers are formed from a bidirectional functionally graded(FG) layer and a graphene platelet(GPL) reinforced porous layer, respectively. Henceforth, the combined layers will be referred to as a two-dimensional(2D) FG/GPL plate. Two types of porosity and three graphene dispersion patterns, each of which is distributed through the p...     

Perturbation methods for the analysis of the dynamic behavior of damaged plates

This paper presents an analytical method for the analysis of the dynamic behavior of damaged plates. The proposed approach allows the derivation of mode shapes and corresponding curvature modes for plates with various kinds of defects. Damage is modeled as a localized reduction in the plate thickness. Both point and line defects are considered to model notches or line cracks and delaminations in the plate. Small thickness reductions are considered so that the dynamic behavior of the damage plate can be analyzed through perturbations with respect to the undamaged modes. Results are presented to demonstrate the sensitivity of the curvature modes with respect to the considered low damage levels. Also, the curvature modes are used for the estimation of the strain energy of the plate and for the formulation of a damage index which can be used to provide damage location and extent information.     

Crack identification in double-cracked plates using wavelet analysis

In this paper, vibration first mode of a plate with two all-over part-through cracks are analyzed by using discrete wavelets transform of Spline, Haar, Harmonic and Duabechies. It is observed that crack locations are detectable in values of wavelet coefficients as sudden changes. The sensitivity of the wavelet transform method with respect to the variation in type and scale of wavelet, and the variation in distance between two cracks and relative depth of cracks is also investigated. Finally, a function is proposed for determining crack characteristics by using maximum variations trend of the Spline and Harmonic wavelet coefficients with change in relative depth of cracks.     

Plastic buckling analysis of thick plates using p-Ritz method

This paper is concerned with the application of the p-Ritz method for the plastic buckling analysis of thick plates. In order to allow for the effect of transverse shear deformation in thick plates, the Mindlin plate theory is adopted. The plastic buckling behaviour of the plate is captured by using the incremental and deformation theories of plasticity. The material property of the plate is assumed to obey the Ramberg–Osgood stress–strain relation. The p-Ritz method will be applied to obtain the governing eigenvalue equation for the plastic buckling analysis of uniformly stressed plates with edges defined by polynomial functions. In the p-Ritz method, the displacement functions of the plate are approximately represented by the product of mathematically complete two-dimensional polynomial functions and boundary equations raised to appropriate powers that ensure the satisfaction of the geometric boundary conditions. The validity, convergence and accuracy of the method were demonstrated for various plate shapes such as rectangular, triangular and elliptical shapes. A parametric study was also undertaken to study the plastic buckling behaviour and the effect of transverse shear deformation.     

Transient dynamic response of debonded sandwich plates predicted with finite element analysis

Dynamic transient response of a composite sandwich plate with a penny-shaped debonded zone has been studied by using the finite element analysis within the ABAQUS/Explicit code in this paper. In order to accurately predict the response of the debonded sandwich plate to impulsive loading, contact–impact and sliding conditions along the damaged skin-to-core interface were imposed in the model through a kinematic predictor/corrector contact algorithm. The accuracy of the finite element (FE) model used was verified by comparing between numerical predictions and experimental data known in literature for the frequency spectrum of a cracked polycarbonate laminated beam containing a delamination. By analyzing nonlinear aspects of the transient dynamics of the sandwich plate, it is shown that the presence of the debond significantly alters its short-term response. In this respect, a considerable influence of contact events within the debonded region on the plate’s global dynamic response was found out. These results were presented in both time and frequency domains. The predictions performed also showed that the FE model applied would be useful for nondestructive evaluation of defects in composite sandwich plates, and for studying dynamic response of such plates to impact.     

On plastic dynamic flexure of plates

Summary This paper discusses the rigid-plastic flexure of plates subjected to dynamic loading. A piecewise linear yield surface and small displacements are assumed. The plate is discretized by assuming the constant moment mixed triangular element of Herrmann. Under the above assumptions the dynamic loading of plates is turned into a problem in linear inequalities which is a priori discretized in time. An approximate technique is developed, which takes into account the influence of the strain-hardening and the strain rate sensitivity of material. Some numerical examples of plates subjected to a given velocity distribution confirm the efficiency of this approach.

---

Sommario Si analizza il problema della flessione rigidoplastica di una lastra soggetta a carichi dinamici. La lastra viene discretizzata assumendo l'elemento triangolare misto a stato di sollecitazione costante di Herrmann. Tale assunzione insieme alle ipotesi di piccoli spostamenti e di superficie di plasticizzazione lineare a tratti, consente di ricondurre il caricamento dinamico della lastra ad un problema retto da diseguaglianze lineari, che risulta discretizzato a priori nel tempo. Attraverso una tecnica approssimata si valuta l'influenza che hanno sulla risposta dinamica della struttura, l'incrudimento e la sensibilità alle velocità di deformazione del materiale. L'efficienza del procedimento è verificata attraverso alcuni esempi numerici di lastre di diversa geometria sottoposte ad una prefissata distribuzione di velocità.

---

---

Research supported by the National Research Council (C.N.R.P.A.d.I.S.) of Italy.