An optimal control approach to the analysis of inelastic structures under cyclic loading

Optimal control theory is used to study the asymptotic behaviour of elasto-viscoplastic structures under cyclic loading. With this approach, the asymptotic state is found as the solution of a minimization problem. General properties of this method are established. A simple thermomechanical problem is studied to illustrate and validate this approach. An interest of the proposed method lies in its capacity to handle other nonlinearities than plasticity. To illustrate this point, the approach is extended to the coupled viscoplasticity/frictionless contact problem. Some numerical results are given for an elasto-viscoplastic half-plane under cyclic frictionless indentation.     

Single-frequency vibrations and vibrational heating of a piezoelectric circular sandwich plate under monoharmonic electromechanical loading

The forced monoharmonic bending vibrations and dissipative heating of a piezoelectric circular sandwich plate under monoharmonic mechanical and electrical loading are studied. The core layer is passive and viscoelastic. The face layers (actuators) are piezoelectric and oppositely polarized over the thickness. The plate is subjected to harmonic pressure and electrical potential. The viscoelastic behavior of the materials is described by complex moduli dependent on the temperature of heating. The coupled nonlinear problem is solved numerically. A numerical analysis demonstrates that the natural frequency, amplitude of vibrations, mechanical stresses, and temperature of dissipative heating can be controlled by changing the area and thickness of the actuator. It is shown that the temperature dependence of the complex moduli do not affect the electric potential applied to the actuator to compensate for the mechanical stress __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 1, pp. 79–89, January 2008.     

Flexural vibrations and vibrational heating of a ring plate with thin piezoceramic pads under single-frequency electromechanical loading

The paper deals with the coupled problem of flexural vibrations and dissipative heating of a viscoelastic ring plate with piezoceramic actuators under monoharmonic electromechanical loading. The temperature dependence of the complex characteristics of passive and piezoactive materials is taken into account. The coupled nonlinear problem of thermoviscoelasticity is solved by an iterative method. At each iteration, orthogonal discretization is used to integrate the equations of elasticity and an explicit finite-difference scheme is used to solve the heat-conduction equation with a nonlinear heat source. The effect of the dissipative heating temperature, boundary conditions, and the thickness and area of the actuator on the active damping of the forced vibrations of the plate under uniform transverse harmonic pressure is examined __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 99–108, February 2008.     

A variational approach to the fracture of brittle thin films subject to out-of-plane loading

We address the problem of fracture in homogenous linear elastic thin films using a variational model. We restrict our attention to quasi-static problems assuming that kinetic effects are minimal. We focus on out-of-plane displacement of the film and investigate the effect of bending on fracture. Our analysis is based on a two-dimensional model where the thickness of the film does not need to be resolved. We derive this model through a formal asymptotic analysis. We present numerical simulations in a highly idealized setting for the purpose of verification, as well as more realistic micro-indentation experiments.     

Plastic strip model of circular crack under cyclic loading with damage accumulation

A cylindrical solid containing a penny-shaped crack in its mid plane is subjected to a remote tensile stress field. In the plastic region near the crack border, damage due to continuous deterioration of the material accumulates, and may lead to crack instability and crack growth. A damage model relating the crack opening displacement in the plastic zone to the fraction of the cross-sectional area occupied by voids is used to describe the conditions necessary for the onset of crack instability, fatigue crack propagation by cyclic loading, and rates of crack growth for time-dependent environmental effects.     

Delayed fracture of an isotropic viscoelastic material with a crack under cyclic loading

The delayed fracture of an isotropic viscoelastic plate is examined as a process involving the subcritical propagation of a straight normal-rupture crack during fatigue loading. Calculations are based on the modified {ie165-1} of fracture, it being assumed that the size of the prefracture zone ahead of the moving crack remains constant. This zone is also assumed to be small compared to the size of the crack itself. Solutions for a time-dependent crack length are given both for media which undergo quasi-viscous flow (an integral operator with an Abelian kernel is used) and for media whose creep curves have a horizontal asymptote (an integral operator with a kernel in the form of the fractional-exponential function of Yu. N. Rabotnov is used). S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 2, pp. 60–64, February, 1999.     

Development of a smart composite pipe joint integrated with piezoelectric layers under tensile loading

To actively reduce the stress concentration effect in adhesive layers, a novel smart adhesively bonded composite pipe joint system was developed by integrating piezoelectric layers as sensor/actuator in the connection coupler. In the presently developed smart pipe joint system, the mechanical loading induced structural deformation can be detected and monitored by integrated sensing piezoelectric layers, and then the signal is fed back to the integrated actuating piezoelectric layers to adaptively produce additional forces and moments so as to decrease the maximum peel and shear stresses in the adhesive layer. In order to theoretically predict the efficiency of the developed smart pipe joint system, an electro-mechanical theoretical analytical model was established to investigate the characteristics of the joint system under end tension load in terms of first-order shear deformation theory. Simultaneously, the state-space method was utilized to deduce the final analytical solutions, including the peel and shear stress distributions in the adhesive layer. Finally, some detailed numerical results were obtained to demonstrate the optimal design method of such smart pipe joint system and further validate the integrity of this joint system.     

Dynamic carrying capacity of thin inelastic circular plates with respect to strength and deformability

We take into account thin flexible circular plates, which deform elastic-visco-plastically under high intensity external loading and in which volume damage can occur. The plates are submitted to uniformly distributed impulsive loading. The plate-carrying capacity is determined in accordance with deformation and strength criteria. Our purpose is to obtain the relation between the geometrical sizes and the material characteristics of the plate on one hand and the dynamic impulse parameters (amplitude and duration) on the other, when the plates lose their carrying capacity.     

Inverse approach to identification of material parameters of cyclic elasto-plasticity for component layers of a bimetallic sheet

The present paper proposes a novel approach to the identification of the mechanical properties of individual component layers of a bimetallic sheet. In this approach, a set of material parameters in a constitutive model of cyclic elasto-plasticity are identified for the two layers of the sheet simultaneously by minimizing the difference between the experimental results and the corresponding results of numerical simulation. This method has an advantage of using the experimental data (tensile load vs strain curve in the uniaxial tension test and the bending moment vs curvature diagram in the cyclic bending test) for a whole bimetallic sheet but not for individual component layers. An optimization technique based on the iterative multipoint approximation concept is used for the identification of the material parameters. This paper describes the experimentation, the fundamentals and the technique of the identification, and the verification of this approach using two types of constitutive models (the Chaboche-Rousselier and the Prager models) for an aluminum clad stainless steel sheet.     

Non-uniform frictional sliding under cyclic loading with frictional characteristics changing in the process of sliding

Frictional sliding on a crack with non-uniform frictional characteristics is considered. The present work continues the investigation of Gorbatikh et al. [Int. J. Solids Struct., in press] and focuses on the cyclic loading. The evolution of the sliding process in loading–reloading–unloading cycles is analyzed. We also extend the analysis to the important case when the frictional resistance changes in the process of sliding (such changes may model “degradation” of the sliding surface during sliding, as well as other physical factors, not necessarily related to the sliding itself).     

Stress analyses of a smart composite pipe joint integrated with piezoelectric composite layers under torsion loading

In order to improve the joint failure strength, an adhesively bonded smart composite pipe joint system has been developed by integrating electromechanical coupling piezoelectric layers with the connection coupler. It has been validated that the integrated piezoelectric ceramic layers can smartly reduce stress concentration in the adhesive layer bond-line under bending or axial tension loads. In this study, piezoelectric particle/fiber reinforced polymer composite was utilized to construct adhesively bonded smart composite pipe joint systems, in order to overcome the brittle characteristic of the piezoelectric ceramic layers and to facilitate joint construction. Since torsion is one of the dominating loading conditions in practice, the behavior of the newly developed smart pipe joint system subjected to torsion loading was investigated in-detail to evaluate the effect of the integrated piezoelectric reinforced polymer composite layer on the joint performance. Firstly, based on the first-order shear deformation theory, the fundamental equations with relevant boundary and continuity conditions were developed to theoretically model the smart pipe joint system subjected to torsion loading. Further, the analytical solutions for the mid-plane displacements and the shear and peel stresses in the adhesive layer were obtained by using the Levy solution and the state-space method. Finally, some numerical examples were presented to evaluate the detailed effect of the stacking sequence and thickness of the integrated composite piezoelectric layers in the connection coupler on reducing the stress concentration in the adhesive layer; the effect of the applied electric fields on shear and peel stresses in the adhesive layer was also illustrated.     

Studying the forced vibrations of fluid-filled cylindrical shells with regard to the nonlinear interaction of different flexural modes

The paper is concerned with the forced nonlinear multimode vibrations of thin cylindrical shells fully filled with a perfect incompressible fluid. The frequency response characteristics of shells undergoing steady-state vibration as simple (standing wave) and compound (traveling wave) deformation modes are plotted and examined __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 8, pp. 97–106, August 2006.     

A Green's function approach to the deflection of a FGM plate under transient thermal loading

Summary  Green's function approach is adopted for analyzing the deflection and the transient temperature distribution of a plate made of functionally graded materials (FGMs). The governing equations for the deflection and the transient temperature are formulated into eigenvalue problems by using the eigenfunction expansion theory. Green's functions for solving the deflection and the transient temperature are obtained by using the Galerkin method and the laminate theory, respectively. The eigenfunctions of Green's function for the deflection are approximated in terms of a series of admissible functions that satisfy the homogeneous boundary conditions of the plate. The eigenfunctions of Green's function for the temperature are determined from the continuity conditions of the temperature and the heat flux at interfaces. Received 9 October 2000; accepted for publication 3 April 2001