This paper deals with the simulation methodology of large and complex structures with multiple contacts and wear. The methodology developed is used to evaluate the dynamics and wear of gas turbine combustors. A unified approach of representing multiple rigid/elastic bodies with numerous contacts is developed. Representation is made, too, of the changing nature of these contacts — both geometric and material. The entire methodology is implemented in a generic and easy-to-use simulation code which serves as a useful generic design/analysis evaluation tool MAP (Mechanism Analysis Program). Appropriate analytical models for inter-material constitutive laws — both incremental (contact friction, pressure, damping, etc.) and cumulative (wear theories) — are incorporated in the tool. As applications of this approach, dynamic simulations of two different gas turbine combustor designs are run, and comparisons are made with real systems. Excellent correlations have been obtained, both with respect to laboratory test (accelerometer) data, and wear patterns at various contacts and junctions on field samples.

A computational procedure is proposed to determine effective constitutive relations for composite laminates with progressive cracking. The procedure is based on the assumption that the effective stiffness of a cracked ply in a laminate can be determined by analyzing the cracked ply by itself independent of the rest of the laminate. A polynomial failure criterion is used to predict ply cracking using effective ply stresses. The procedure provides a full set of effective laminate stiffnesses as well as crack densities in constituent plies.

A well-aimed layout of fibre-reinforced lightweight rollers does not only require an efficient structural analysis procedure but also the application of structural optimization methods. Therefore, an analytical procedure is introduced for the calculation of the static behaviour of cylindrical shells subject to axisymmetric and/or nonaxisymmetric loads. In the scope of this procedure, arbitrary, unsymmetrical laminates as well as various boundary conditions will be considered. Basis is the shell theory by Flügge enhanced by anisotropic constitutive equations (material law) in the scope of the classical laminate theory. By means of mathematical optimization procedures we then determine optimal lightweight rollers, using different design and evaluation models. For that purpose, coated and uncoated roller constructions as well as hybrid types made of CFRP/GFRP will be applied. Concluding, we will discuss possible improvements and advantages of anisotropic lightweight rollers in contrast to isotropic ones made of steel or aluminium.

Thermal deflections of symmetrically laminated plates that are continuous over many line supports are determined using the Rayleigh-Ritz method. The constitutive equations and the thermal loads are expressed in terms of four non-dimensional lamination parameters. Layups that minimize thermal deflections are determined for several types of composite plates subjected to temperature increases that vary linearly through the thickness.

In the present investigation the incremental Hellinger-Reissner variational principle, a hybrid-strain based formulation and an updated Lagrangian formulation are adopted to derive explicit expressions for element stiffness matrices of various flat triangular shell finite elements. These elements are developed for application to the analysis of thin and thick shell structures undergoing large geometrically nonlinear deformation at finite strain. Correct representations of finite rotations and the specifically chosen strain field maintain appropriate rigid body motions and prevent shear locking phenomena. Consideration of thickness updating and a finite strain formulation relaxes any plane stress assumptions and enables the analyst to deal with three-dimensional constitutive models. Two numerical examples are presented to demonstrate the performance of the elements.

This paper is concerned with the analysis of active and passive hybrid actions in structures with active constrained damping layers (ACL). A system model is derived via Hamilton’s Principle, based on the constitutive equations of the elastic, viscoelastic, and piezoelectric materials. The model converges to a fully-active piezotronic system as the thickness of the viscoelastic material (VEM) layer approaches zero. A mixed Galerkin-GHM method is employed to discretize and analyze the model in time domain. With an LQR optimal control formulation, the effects of the active constrained layer configuration on the system vibration suppression performance and control effort requirements are investigated. Analysis illustrate that the active piezoelectric action with proper feedback controls will always enhance the damping ability of the passive constrained layer. On the other hand, the viscoelastic layer will reduce the direct control authorities from the active source to the host structure. The significance of this effect depends very much on the viscoelastic layer thickness and material properties. Therefore, with some parameter combinations, the ACL configuration could require more control effort while achieving less vibration reductions compared to a fully-active system. Through analyzing the performance and control effort indices, the conditions where this active-passive hybrid approach can outperform both the passive and active systems are quantified. Based on this study, design guidelines can be set up to effectively integrate the host structure with the piezoelectric and viscoelastic materials, such that a true active-passive hybrid control system can be achieved.

Optically driven actuators can introduce remote actuation and control effects without any hard-wire connections. In this study, photostrictive { opto-piezoelectric ) characteristics and photodeformation of distributed photostrictive optical actuators are investigated and a parametric study of design parameters is conducted. Photodeformation induced by the photostrictive ( opto-piezoelectric ) effect (a combination of the photovoltaic effect and the converse piezoelectric effect ) is discussed and its two-dimensional (2-D) constitutive relations are presented. 2-D equivalent control forces and moments induced by the photodeformation effect of distributed actuators are formulated, and system governing equations derived. Static and dynamic applications are discussed, and simulation studies of design parameters are conducted and evaluated.

In this paper, the equations of motion governing the transient response of an elastomer rod with embedded shape memory alloy actuators are derived. The elastomeric flexural dynamics and elastomeric thermal dynamics are represented by a pair of parameter-dependent, coupled, partial differential equations. The response of the structural system exhibits strong hysteresis effects due to the nonlinear nature of the constitutive law of the SMA actuator. As opposed to previous work by the authors in which an explicit equation for the nonlinear constitutive law is utilized, the work herein utilizes an integral operator in a phenomenological representation of the hysteresis. Specifically, a static hysteresis operator is employed to represent the current-to-stress transformation in the SMA. The hysteresis operator consequently appears as a control influence operator in the system of governing partial differential equations. This paper presents a two-stage identification process to characterize the multivalued response associated with hysteresis. Preliminary experimental results validate the effectiveness of the method for the class of problems considered.

Failure detection and model updating using structural model are based on the comparison of an appropriate indicator of the discrepancy between experimental and analytical results. The reliability of the expansion of measured mode shapes is very important for the process of error localization and model updating. Two mode shape expansion techniques are examined in this paper : the well known dynamic expansion (DE) method and a method based on the minimisation of errors on constitutive equations (MECE). A new expansion method based on some improvements of the previous techniques is proposed to obtain results that are more reliable for error localisation and for model updating. The relative performance of the different expansion methods is demonstrated on the example of a cantilever beam.

A numerical algorithm for uni-axial inelastic wave propagation due to impact-type loading is presented. The algorithm is based on the linear-elastic multiple-field formulation, in which inelastic parts of strain are considered as eigenstrains acting upon a linear-elastic background structure. The solution thus can be consistently found by superposition of altogether elastic waves, where the fictitious eigenstrains are calculated from the inelastic constitutive equations by numerical integration. Due to the physical background of the method, the procedure turns out to be both, computationally accurate and numerically stable. In the present contribution, the algorithm is realized in C++ and applied to the loading-unloading problem of a semi-infinite rod of Maxwell material. The accuracy of the algorithm is demonstrated by comparing to an analytic solution which is derived in the form suitable for comparison.

Non-contact light activated distributed opto-electromechanical actuators represent a new class of precision distributed actuator which are based on the photodeformation process and controlled by high energy lights, e.g., lasers and ultra-violet lights. Fundamental opto-thermo-electromechancial constitutive relations are discussed and formulations of optically induced control forces and moments introduced. Mathematical modeling and analysis of distributed opto-electromechanical shell actuators are presented. A generic distributed photo-actuation theory is proposed and the closed-loop opto-thermo-electromechancial equations of circular cylindrical shells are derived. The systems equations reveal the couplings among elasticity, photodeformation, pyroelectricity, and thermoelasticity. Active distributed control of flexible cylindrical shells using segmented distributed opto-electromechanical shell actuators are investigated and the control effectiveness is evaluated. Membrane and bending control effects are evaluated. Time history analyses of independent modal control reveal that the Lyapunov control is more effective than the proportional feedback control.

A time finite element method is developed for the steady-state solutions of vibrating elastic mechanisms. The governing equations of motion for each individual link are described in a link (local) coordinate system with constant coefficients. The set of second order differential equations for all links are then coupled by a set of constitutive equations of elastic joint models describing the link interconnections. In utilizing time finite elements which discretize the forcing time period into a number of time intervals, the elastic motion is approximated by a set of temporal nodes of all spatial degrees of freedom of the mechanism system. The result is a set of linear algebraic system with a sparse structure and that can be solved effectively. A scotch york mechanism and a four-bar linkage are included as examples to illustrate the modeling and solution procedures applied.

The dynamic response and stability of parametrically excited viscoelastic belts are investigated in this paper. The linear viscoelastic differential constitutive law is employed to characterize the material property of belts. The generalized equation of motion is obtained for a viscoelastic moving belt with geometric nonlinearity. The method of multiple scales is applied directly to the governing equation, which is in the form of continuous gyroscopic systems. Closed-form expressions for the amplitude, existence conditions and stability conditions of non-trivial limit cycles of the summation resonance are obtained. Effects of viscoelastic parameters, excitation frequencies, excitation amplitudes and axial moving speeds on stability boundaries are discussed.

A mathematical model of track-wheel-terrain interaction is presented herein to support the dynamic simulation of tracked vehicles. This model combines approximate and known constitutive laws for terrain response with a new representation for the track element. The resulting track-wheel-terrain model allows the computation of the track tension and the normal and shear forces at the track-terrain interface as the track negotiates terrain of arbitrary profile. A key feature of this model is the uniform treatment of contact between the track and the roadwheels and the track and the terrain. Treating both contact problems in the same manner significantly simplifies the problem formulation and also reduces difficulties in computing points of track-wheel and track-terrain separation. The model takes the form of a two-point nonlinear boundary value problem that accounts for tension variations along the track (due to the non-uniformly distributed normal pressure and traction), track extensibility, and geometrically large (nonlinear) track deflections. Solutions are obtained using a finite element formulation. Both the model and the solution method are formulated with a view towards implementation within a multibody dynamics code for simulating a full vehicle. Several examples illustrate the capabilities of the proposed model.

This article illustrates the nonlinear response of a hysteretic two degree of freedom system. The constitutive laws which define the force-displacement relation are based on a hysteretic model with Masing rules linked to a suitable nonlinear elastic model. Attention is focused on the periodic response, though an insight is also given to the non-periodic response. The method of analysis used is the harmonic balance with many components. Frequency-response curves are evaluated for different system characteristics. Ratios of small amplitude vibration frequency 3 and 2 are considered, with different hysteresis degree. Notwithstanding the dissipation due to hysteresis usually destroys most of the phenomena evidenced by the classical nonlinear oscillators, in the present analysis a rich behavior is found: IT symmetric and non symmetric, 2T periodic responses are found and so on.

This paper describes the cyclic accumulative plastic strain in a polycrystalline material when subjected to loading conditions promoting ratcheting behavior. For this purpose, a unified viscoplastic constitutive model based on non-linear kinematic hardening formulation is implemented. Identification of the model parameters was carried out using an experimental program that included monotonic, cyclic and relaxation testing. Simulation of the material response using the proposed model is compared with experimental results for the same loading. This comparison is used to evaluate the model validity.

Energy preserving/decaying schemes are presented for the simulation of the nonlinear multibody systems involving shell components. The proposed schemes are designed to meet four specific requirements: unconditional nonlinear stability of the scheme, a rigorous treatment of both geometric and material non-linearities, exact satisfaction of the constraints, and the presence of high frequency numerical dissipation. The kinematic nonlinearities associated with arbitrarily large displacements and rotations of shells are treated in a rigorous manner, and the material nonlinearities can be handled when the constitutive laws stem from the existence of a strain energy density function. The efficiency and robustness of the proposed approach is illustrated with specific numerical examples that also demonstrate the need for integration schemes possessing high frequency numerical dissipation.

Experimental studies of piezo-beam systems subjected to weak harmonic electric fields have revealed typical nonlinear effects, e.g. dependence of the resonance frequency on the amplitude, superharmonics in spectra and a nonlinear relationship between excitation voltage and vibration amplitude. In contrast to the well-known nonlinear effects for piezoceramics in presence of strong electric fields, these effects have not been widely described in the literature. In this paper we attempt a description of these phenomena by nonlinear constitutive relations, in particular by a non-constant elastic modulus E c and piezoelectric factor d 31 . The equations of motion for the system under consideration are derived via the Ritz-method using Hamilton’s principle. The ‘nonlinear’ parameters are determined and the numerical results are compared to those obtained experimentally. The effects described herein may have a significant influence whenever structures are excited close to resonance frequencies via piezo-electric elements.

This investigation focuses on the development of unified techniques for mathematically modeling the hysteresis and constitutive nonlinearities inherent to ferroelectric, ferromagnetic and ferroelastic materials at moderate to high drive levels. Motivating materials include piezoceramics, relaxor ferroelectrics, magnetostrictives and shape memory alloys, but the modeling approach is sufficiently general to include a large variety of ferroic compounds. The nonlinear and hysteretic behavior of these materials can be attributed to their underlying domain structure and this common ferroic framework is utilized to construct unified constitutive models for the materials. These models are constructed in two steps. In the first, thermodynamic principles are employed to quantify the anhysteretic behavior which would result in the absence of inclusions in the material. In the second step, energy relations are employed to quantify the irreversible and reversible motion of domains walls about pinning sites in the material. The resulting models are formulated as low-order ordinary differential equations. The performance and behavior of the models are illustrated for piezoceramic, magnetostrictive and shape memory compounds.

Based on Von Karman strain-displacement relations and variational principles, the FEM formulations, which are used to analyze the thermal buckling, and thermal postbuckling of composite plates with embedded SMA are presented in this study. The recovery stress and young modulus are calculated by one-dimensional constitutive model. Some numerical examples are also presented. The results indicate that activated SMA can suppress the thermal buckling of the plates and reduce thermal postbuckling deflections.