New designs of revetments for the earth slopes at the Zagorsk pumped-storage station

Conclusions  

FDM analysis for MHD flow of a non-Newtonian fluid for blood flow in stenosed arteries

A computational model is developed to analyze the effects of magnetic field in a pulsatile flow of blood through narrow arteries with mild stenosis, treating blood as Casson fluid model. Finite difference method is employed to solve the simplified nonlinear partial differential equation and an explicit finite difference scheme is obtained for velocity and subsequently the finite difference formula for the flow rate, skin friction and longitudinal impedance are also derived. The effects of various parameters associated with this flow problem such as stenosis height, yield stress, magnetic field and amplitude of the pressure gradient on the physiologically important flow quantities namely velocity distribution, flow rate, skin friction and longitudinal impedance to flow are analyzed by plotting the graphs for the variation of these flow quantities for different values of the aforesaid parameters. It is found that the velocity and flow rate decrease with the increase of the Hartmann number and the reverse behavior is noticed for the wall shear stress and longitudinal impedance of the flow. It is noted that flow rate increases and skin friction decreases with the increase of the pressure gradient. It is also observed that the skin friction and longitudinal impedance increase with the increase of the amplitude parameter of the artery radius. It is also found that the skin friction and longitudinal impedance increases with the increase of the stenosis depth. It is recorded that the estimates of the increase in the skin friction and longitudinal impedance to flow increase considerably with the increase of the Hartmann number.     

Effective elastic properties of damaged isotropic solids

In continuum damage mechanics, damaged solids have been represented by the effective elastic stiffness into which local damage is smoothly smeared. Similarly, damaged solids may be represented in terms of effective elastic compliances. By virtue of the effective elastic compliance representation, it may become easier to derive the effective engineering constants of damaged solids from the effective elastic compliances, all in closed form. Thus, in this paper, by using a continuum modeling approach based on both the principle of strain energy equivalence and the equivalent elliptical micro-crack representation of local damage, the effective elastic compliance and effective engineering constants are derived in terms of the undamaged (virgin) elastic properties and a scalar damage variable for both damaged two- and three-dimensional isotropic solids.     

Spectral element analysis for an axially moving viscoelastic beam

In this paper, a spectral element model is derived for the axially moving viscoelastic beams subject to axial tension. The viscoelastic material is represented in a general form by using the one-dimensional constitutive equation of hereditary integral type. The high accuracy of the present spectral element model is verified first by comparing the eigenvalues obtained by the present spectral element model with those obtained by using the conventional finite element model as well as with the exact analytical solutions. The effects of viscoelasticity and moving speed on the dynamics of moving beams are then numerically investigated.     

Spectral element model for axially loaded bending–shear–torsion coupled composite Timoshenko beams

The use of frequency-dependent spectral element matrix (or exact dynamic stiffness matrix) in structural dynamics is known to provide extremely accurate solutions, while reducing the total number of degrees-of-freedom to resolve the computational and cost problems. Thus, in this paper, the spectral element model is developed for an axially loaded bending–shear–torsion coupled composite laminated beam which is represented by the Timoshenko beam model based on the first-order shear deformation theory. The high accuracy of the spectral element model is then numerically verified by comparing with exact theoretical solutions or the solutions obtained by conventional finite element method. For the numerical verification, the finite element model is also provided for the composite laminated beam.     

A theory of smeared continuum damage mechanics

This paper considers smeared continuum damage mechanics based on the equivalent elliptical crack representation of a local damage. This approach provides a means of utilizing the crack energies derived in fracture mechanics, and of identifying the local damage state from local stress and strain information. The strain energy equivalence principle is used to derive the effective continuum elastic properties of a damaged solid in terms of the undamaged elastic properties and a scalar damage variable. The scalar damage variable is used to develop a consistent damage evolution equation. The combination of representing local damage as an equivalent elliptical crack, the determination of effective elastic properties using a strain energy equivalence principle, and a consistent damage evolution equation yields a simple, yet powerful local approach for continuum damage analysis     

Vibration analysis of the plates subject to distributed dynamic loads by using spectral element method

A spectral element method (SEM) is introduced for the vibration analysis of rectangular plates under distributed dynamic loads. In this paper, the spectral plate element matrix (often called the dynamic stiffness matrix) is formulated from the relation between the forces and displacement along the opposite two parallel edges. The distributed dynamic load is discretized into a sequence of equivalent line loads. The plate is then considered as a connection of two spectral plate element with the joint node line along which the equivalent line load acts. The spatial coordinate dependence of each equivalent line load is then removed through the spatial Fourier transformation so that the plate (2-D) problem becomes a simplified equivalent beam like (1-D) problem. The remaining solution procedures is therefore the same as that used for beam problems. Numerical tests show that the present SEM provides very accurate solutions when compared to finite element solutions.