Experimental-theoretical correlations of impulsively loaded clamped circular plates

Clamped circular plates are impulsively loaded with sheet explosive, and the resulting large-defection response is monitored using a high-speed streak camera, and dynamic-strain measurements. Dynamic and final-plate deflections as well as strain-time histories of various locations on the plates are compared to deflections and strains obtained with the elastic-plastic structural computer program DEPROSS. It is shown that DEPROSS adequately computes the dynamic response of this highly nonlinear biaxial-stress problem.     

Shape forming of shock wave loaded viscoplastic plates

If metal plates are subjected to impulsive loadings a conical shape of the inelastic deformed plates can occur. In the contrary quasi-statically loaded structures, show a more spherical shape of their inelastic deflections. In the present study, an explanation for the development of conical shapes in the case of shock wave loaded plates is proposed based on wave propagation phenomena. The effect of shape forming is studied experimentally with a shock tube and numerically with finite element simulations.     

Finite viscoplastic deflections of an impulsively loaded plate by the mode approximation technique

The application of the mode approximation technique to a fully clamped circular plate is here described. Mode solutions for finite deflections are obtained from a sequence of instantaneous modes. Master solutions for chosen initial velocity amplitudes are constructed in nondimensional form. These depend weakly on a parameter of viscoplastic material behavior and size of structure, and so can be applied to a variety of loadings and structures. Finding each instantaneous mode shape and acceleration constitutes an eigenproblem, solved by finite elements with iterations. Comparisons with recent tests on steel and titanium plates are discussed in some detail.     

Post-failure response of impulsively loaded clamped beams

This paper analyses the response of a clamped rigid, perfectly plastic beam subjected to an impulsive velocity loading throughout the span. A critical velocity is determined using a damage mechanics model, beyond which a beam fails at the supports. Attention is focused on the dynamics of the beam after failure. A transient phase of deformation develops after failure and leads to a change of the beam geometry after failure. Other parameters such as the residual kinetic energy and rigid body velocity are also determined. A comparison is made between the clamped case here studied and the simply supported one described elsewhere by the authors.     

Optimal design of impulsively loaded plastic beams for asymmetric mode motions

Optimal design of a rigid-plastic stepped beam is discussed assuming the mode form of motion. Such beam dimensions are sought for which a minimum of local or mean deflection is attained within designs of constant volume. It is assumed that the prescribed kinetic energy is imparted to the structure at the initial instant with free motion occurring afterwards. It is shown that besides three symmetric modes of motion, also the asymmetric modes may exist. An optimal design for asymmetric modes is determined and compared with a respective design for symmetric modes, obtained previously in [1].     

Bounds for finite deflections of impulsively loaded structures with time-dependent plastic behaviort

The paper shows that upper bounds on deflections of an impulsively loaded structure whose behavior in the plastic range is strain rate dependent may be obtained by an application of the theorem of minimum potential energy, with results valid for finite deflections and strains. The concepts of extremal path behavior in strain-time space, due to Ponter, are used in order to provide unique definitions of strain energy and complementary energy for the path dependent material. The theorems are illustrated by examples of fully constrained beams in which deflections of the order of the beam thickness lead to large forces of membrane type.     

Perturbation analysis for the postbuckling of rectangular orthotropic plates

In this paper, applying perturbation method to von Kármán-type nonlinear large deflection equations of orthotropic plates by taking deflection as perturbation parameter, thé postbuckling behavior of simply supported rectangular orthotropic plates under inplane compression is investigated. Two types of in-plane boundary conditions are now considered and the effects of initial imperfections are also studied. Numerical results are presented for various cases of orthotropic composite plates having different elastic properties. It is found that the results obtained are in good agreement with those of experiments.     

Evaluation of viscoplastic parameters and its application for dynamic behaviour of plates

Summary  The evaluation of material parameters for viscoplastic Chaboche and Bodner-Partom formulations is carried out using tensile tests only. The determination of the Bodner-Partom law is quite easy. The parameter study for the Chaboche law usually requires carrying out strain-controlled cyclic tests. In this work, we propose supporting this type of experiments by numerical simulations. A set of parameters for each formulation is identified for steel, and is used to calculate the dynamic behaviour of circular plates. The results are compared with the experimental data on steel plates. Received 27 April 1999; accepted for publication 7 October 1999     

Determining the model parameters of nonlinear deformation of isotropic and composite materials from the results of an experimental-computational analysis of impulsively loaded circular plates

A method for identifying the material parameters of the constitutive relations of viscoelastic and elastoplastic deformation for isotropic and homogeneous composite materials is developed based on minimizing the mismatch between the results of numerical and experimental modeling of unsteady deformation of structural elements made of the materials studied. The method is tested and shown to be effective in determining the viscoelastic and elastoplastic characteristics of models for the nonlinear deformation of impulsively loaded isotropic and composite circular plates.     

Creep of concentrically loaded circular plates

Using a strain-energy approach and the Rayleigh-Ritz procedure, a nonlinear compressible theory was developed to predict the creep deflections of circular plates laterally loaded by a point force acting at the center of the plates. Both clamped and simply supported boundary conditions were considered. The theory applies to transient as well as to steady-state creep. The stress-strain-time relations for the material were represented by a family of isochronous stress-strain curves. For analytical purpose, each curve was approximated by an arc hyperbolic sine function. Experimental data were obtained from eight plates made of high-density polyethylene tested in a controlled-atmosphere room. Material properties were obtained from tension and compression specimens. All test members were subjected to the same load history. An initial load was held constant for a specified time and then increased by 10 percent of its initial value at four equal intervals of time. Good agreement was found between theory and experiment.     

Experiments on viscoplastic response of circular plates to impulsive loading

Tests are described of circular plates of mild steel and commercially pure titanium loaded impulsively by means of explosive sheet. Three loading geometries were used, with magnitudes such that final deflections in the range from one to about seven plate thicknesses were produced. Clamping against radial as well as transverse deflections at the edge was provided. Both materials exhibit strong plastic rate sensitivity. Parameters describing this behavior were obtained from stress-strain tests at low to intermediate rates together with published data for high strain rates. The measured final deflections and response times are compared with predictions of the mode approximation technique as extended to large deflections of viscoplastic structures.     

复合材料层合板的摄动随机Cell-Based光滑有限元

随机性是实际工程结构的固有特性,如何更真实地描述含随机参数结构的随机响应及统计特性,对工程结构的可靠性设计具有非常重要的意义。本文基于Cell-Based光滑有限元,采用四边形单元,推导了基于一阶剪切变形理论的复合材料层合板的光滑有限元公式,降低了网格划分要求,适应不规则网格,并采用离散剪切间隙有效地消除了剪切自锁;结合摄动法和随机场理论,导出了复合材料层合板的摄动随机光滑有限元平衡方程,并给出了结构随机响应数字特征的计算公式,求解了材料属性含随机性的复合材料层合板的随机响应问题,数值算例结果表明了本方法的有效性和准确性。     

Elastic-plastic analysis of biaxially loaded center-cracked plates

Center-cracked panels loaded in biaxial tension are examined in this paper. Calibration relations for the J integral and the Q constraint factor are presented for a Ramberg–Osgood power law hardening material under plane stress and plane strain loadings. Two cases are examined: an isolated crack and a periodic array of cracks both under biaxial loading conditions. The latter has previously been studied for plane stress conditions. A number of different J estimation schemes are proposed based on the remote load and displacement and their dependence on geometry, biaxiality, and material properties is discussed. The variation of constraint, as characterised by Q, is also presented for plane stress and plane strain conditions. Simple slip line field solutions are derived for perfectly plastic conditions and the resulting limit load solutions are compared with numerically determined values. Implications for failure of cracked plates under biaxial loading are discussed.     

Birefringent-coating analysis of laterally loaded perforated plates

The purpose of this investigation was to obtain experimental stress and deflection data for thick, circular, simply supported plates, containing circular transverse perforations in square motif, under uniform lateral loading. The stress-concentration factor and the deflection-multiplier factor, the ratio of the maximum principal stress and the maximum deflection of the perforated plate to that of the solid-plate specimen, respectively, were obtained for each perforated specimen. These factors can be conveniently used for the design of tube sheets, perforated heads, or other similar structural components.     

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.     

The non-linear,dynamic response of an impulsively loaded circular plate with a central hole

A numerical method, called Direct Analysis, is described and applied to solve the problem of a plate undergoing a large impulsive load. For generality, an expanded, non-linear form of the equations of motion is used and shear correction and rotatory inertia are considered. The wave speeds are calculated from the non-linear equations and appropriate boundary conditions are applied so that reflected waves are included. The results for two types of step loading pulses are presented and compared with previously presented solutions. The response of the plate is discussed and conclusions as to the effects of the non-linearities are given.