Distortional Model Research Articles

A simplified distortional buckling model for doubly symmetrical I-sections

Lateral torsional instability of I-beams considers the relative displacement of the unstable compression flange to the stable tension flange. It is commonly assumed that little or no distortion takes place between the two flanges. In this paper, an approach is proposed whereby the section properties that control lateral torsional buckling are adjusted to allow for the influence of cross-section distortion, by the use of simple spring models representing the relative stiffness of the flanges and the web. The model is developed for elastic, inelastic, and plastic cases and compared with the results obtained from finite element models developed by other researchers. A method of quantifying the lateral distortional buckling resistance of I-beams is of particular importance in the hogging moment region of continuous composite beams; the ability of the proposed model to deal with this complex problem has been previously demonstrated by the authors. In this paper, the proposed model is used to illustrate the influence of distortional buckling on doubly symmetrical I-sections.Key words: lateral, distortional, I-beams, elastic, inelastic.

A simplified distortional buckling model for doubly symmetrical I-sections

A simplified distortional buckling model for doubly symmetrical I-sections

Ultrasonic Nondestructive Evaluation of Microstructural Property Changes of Plastically Deformed Solid under Combined Stress States.

Ultrasonic wave velocities in a plastically deformed medium are known to depend upon its microstructural properties. Therefore, one of the authors proposed a theoretical model of an ultrasonic nondestructive method in order to evaluate plastically deformed states. We obtained good agreement between the numerical and experimental results for an aluminum alloy specimen subjected to uniaxial tension and reported the influence of annealing upon plastic anisotropy and the correlation between the Lankford's value and the shape of yield surface of the specimen. In order to verify the proposed theory we simulated using the internal state variables of an anisotropic distortional yield model longitudinal wave velocities under combined stress states and the subsequent yield surfaces, which were determined to agree well with the experimental results of the longitudinal and transverse wave velocity changes under uniaxial tension test, and then compared the simulated results with experimental results of the longitudinal wave velocity and the yield surface of the aluminum alloy tested in combinations of tension or compression and torsion.

Constitutive modelling for granular media using an anisotropic distortional yield model

It has been attempted here to model the mechanical response of granular media through a combination of analytical, numerical and experimental techniques. Based on the experimental evidence obtained from a series of triaxial laboratory experiments on specimens made of glass beads, the model attempts to simulate the movement of yield surfaces and the stress-strain relationships. It is found that the yield surface distorts in the direction of loading in a manner analogous to that of metals. An anisotropic distortional yield model is formulated in order to describe the experimental behavior exhibited by these granular media. From the experimental yield surfaces the parameters of the model have been evaluated and a hardening rule, based on the Phillips rule, has been determined. Associativity on the π-plane has been observed experimentally. Using these concepts the constitutive formulation has been presented and the stress-strain curves have been generated. From the comparisons of these curves we observe a good correlation between the model and the experimental observations.

Wave motion and its dispersive properties in a finite element model with distortional elements

Solutions are obtained for wave motion in a hybrid-mass distortional finite element model by employing the extended method of lattice dynamics. The dispersion equations of wave motion are also given through the solutions. The dispersive properties of a plane wave and the existential condition of an inhomogeneous wave are studied. The results show that the ability of the hybrid-mass model to resist the distortion of element shape is greater than that of the consistent-mass model but lower than that of the lumped-mass model. The velocities of wave propagation in the lumped-mass model are not always lower than that in the corresponding continuum. When the element shape is highly distorted, the velocities in the lumped-mass model may exceed those in the continuum. The effects of discretization in time domain on wave propagation are also discussed.

Experimental Verification of Yield Surfaces Estimated by Ultrasonic Evaluation Method.

Ultrasonic wave velocities in a plastically deformed medium are known to be dependent upon its microstructual material properties, e. g., crystalline structure, texture, distributions of residual stress and vacancy. Therefore, the authors proposed the theoretical modeling of an ultrasonic nondestructive method to evaluate plastically deformed states ; we obtained good agreement between the numerical and experimental results on an aluminum alloy specimen subjected to uniaxial tension, and successively reported the influence of annealing effect upon the plastic anisotropy and the correlation between the Lankford's value and the shapes of yield surface of the aluminum alloy. The purpose of the present paper is to verify the subsequent yield surfaces estimated by the ultrasonic evaluation method, in which the internal variables of the anisotropic distortional yield model were determined to achieve a good fit for the experimental results of the longitudinal and transverse wave velocity changes under the plastic deformation, compared with the experimental yield surfaces of the aluminum alloy tested in combinations of tension or compression and torsion.

Anisotropic Distortional Yield Model

A yield surface model is proposed in this work which may be adapted to both small strain and large strain offset definitions of yielding. The proposed anisotropic distortional yield model is capable of translation, uniform expansion or contraction, as well as distortion of the subsequent yield surface. Two versions of the proposed model are introduced through variations in fourth-order anisotropy tensor M of the yield surface. Experimental observations by Phillips and co-workers (1973, 1974, 1977, 1979, 1985), Helling et al. (1986), and Stout et al. (1985) are taken into consideration in the development of the proposed model. The corresponding fourth-order elastoplastic stiffness matrix is formulated and specific examples are given.

Lattice defects in linear isotropic dielectrics

Using the concept of multipole forces, the problem of dislocations in a linear, isotropic, dielectric material is solved in a closed form. Solutions are also given using the distortional model. Both results are in agreement with each other. The former method has however the advantage to be applicable to all defects. Edge and screw dislocations are solved in details. It is shown that when polarization gradients are accounted for, the Green's function of linear dielectric materials can be determined analytically thus making it possible to solve and explain many phenomena not tractable with other models.

Ballistic limit determination in impacts on multimaterial laminated targets

Two-dimensional numerical analyses have been performed of projectile impacts at 15,00020,000 fps into finite laminated targets consisting of plastic layers backed by aluminum substrates. These analyses used the SHAPE code, with a hydrodynamic-elastic-plastic distortional model. Three solutions are discussed. The first illustrates phenomena occurring during impacts just under the perforation threshold. Results showing the time-resolved development of rear surface bulging are compared with dynamic observations of parallel experiments. Good agreement is obtained. The second and third solutions show conditions leading to perforation. Using a generalized plastic strain criterion, two failure modes are identified. Petalling tends to occur where the plastic front layer of the target is relatively thick and the failure criterion is first exceeded on the back surface near the axis. Plugging occurs in thinner targets when the failure criterion is first exceeded at an off-axis location on the plastic-substrate interface. Through use of SHAPE and this failure criterion, predictions can be made as to whether a given impact will perforate a given multilayered target.