Unit Step Load Research Articles

Dynamic finite element analysis of viscoelastic composite plates in the time domain

AbstractNumerical procedures for analysing transient responses of anisotropic viscoeiastic composite plates have been developed in the time domain using variational principles and a direct time integration method. Recursion relationships have been formulated in order to reduce computer storage substantially. The method developed herein requires only two previous lime solutions to evaluate the next time solution and the necessary storage is independent of the number of the time steps. Verification studies were conducted to evaluate the accuracy and convergence of the present numerical algorithm and they show that the numerical solutions agree well with analytical ones. As examples, dynamic transient responses of viscoeiastic composite plates subjected to unit step loads were calculated using the presently developed procedure.

Singular character of axisymmetric stresses around wedge-shaped notches in cylindrical bodies under torsion: unit step load

Abstract Investigated is the singular character of the stresses as affected by the wedge angle of a sharp notch around cylindrical bodies under torsional loadings. Eigenfunction expansion is used in conjunction with an enriched finite element and the property of a path independent integral to determine the amplitude of the dynamic stress field near a circumferential notch and crack, respectively. A unit step torsional load is applied in both cases. Numerical results are obtained and compared with those in the literature.

Transient waves in a layered anisotropic elastic medium

Wave propagation in a periodically layered medium is studied in which each period consists of two layers of homogeneous anisotropic elastic materials. The layered medium occupies the half-space x ≥ 0 in which the x -axis is normal to the layers. Transient waves in the layered medium are generated by a unit step load in time applied at x = 0. A general solution that applies to any x is obtained in the form of a Laplace transform. Asymptotic solutions valid for large x are then deduced. If the applied load at x = 0 is in the direction of one of the polarization vectors for the layered medium determined here, the stress components propagate uncoupled asymptotically. For general loadings, there are three ‘heads of the pulses’, each of which is in the form of an Airy integral.

The nonlinear interaction between cartilage deformation and interstitial fluid flow

The movement of interstitial fluid through articular cartilage and its influence on the creep behavior of the tissue due to a unit step load function has been investigated. Experimental results are presented to show that the hydraulic permeability of articular cartilage depends on both the axial compressive strain on the tissue sample, as well as the driving pressure difference maintained across the specimen. These experimental results have been utilized in a known theory of a deformable and permeable material used to describe the behavior of articular cartilage. The creep-like behavior of the cartilage in compression has been analytically treated. It has been determined that the nonlinear interaction between the hydraulic permeability of the tissue and the compressive strain on the tissue retards the progress of the consolidation of the cartilage during uniaxial compression. However, the equilibrium displacement of the articular surface as t → ∞ depends only on the elastic constant of the parallel spring and dashpot viscoelastic behavior of the solid component of the tissue.