On nonlinear analysis of elastic shells of revolution.
Elastic shells of revolution axisymmetrically loaded analyzed, using multisegment method for solution of boundary value problems governed by nonlinear differential equations
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Dynamical theory of stability for elastic rods with nonlinear curvature and twist
Considering non-linear terms in the curvature as well as in the twist, the governing boundary value problem for lateral bending of elastic, transverse loaded rods is formulated by means of Hamilton's principle. Using the method of small vibrations, the associated linearized equations of stability are derived, which complete the currently accepted relations. The example of the simplest lateral bending problem illustrates the improved effect of the proposed equations.
Wauer, J.↗
Nonlinear effects of elastic coupling in unsymmetric laminates
Classical lamination theory predicts the room-temperature shape of all unsymmetrically laminated, elevated-temperature cure composites to be a saddle shape. Experimental observation indicates, however, that in many cases the room-temperature shape is cylindrical. In addition, a second cylindrical shape can often be obtained from the first by a simple snap-through action. It is the elastic couplings between inplane and out-of-plane deformations which are inherent in unsymmetric laminates that are responsible for the room-temperature shape. However, the couplings are so strong that geometrically nonlinear effects are produced. These are not accounted for in the classical theory. This paper reviews a theory developed to explain the effects of the coupling on laminate shape. The theory is based on a minimization of the laminate's total potential energy. The theory accounts for geometric nonlinearities. Because the problem is nonlinear, approximate solutions are sought by using a Rayleigh-Ritz procedure. Because of the observed snap-through of some laminates, stability of the predicted shapes is examined. Numerical results and some limited experimental data are presented for several laminates.
Hyer, M. W.↗
An elastic potential for the nonlinear response of unidirectional graphite composites
An elastic potential is proposed that is capable of modeling the reversible portion of the observed nonlinear response of unidirectional graphite fiber composites. The model includes both the stiffening stress-strain behavior as well as the softening Poisson's response for loading in the fiber direction. The model is compared with experimental results for Celion 6000/PMR-15 graphite-polyimide.
Pindera, M.-J.↗
Localized Elasticity Governs the Nonlinear Rheology of Colloidal Supercooled Liquids
Not Available
Kong, Dejia (ORCID:0000000340480208)↗
Nonlinear response of elastic shells status report, 1 feb. - 31 jul. 1967
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De Silva, C. N.↗
A geometrically nonlinear theory of elastic plates
A set of kinematic and intrinsic equilibrium equations is derived for plates undergoing large deflection and rotation but with small strain. The large rotation is treated by the general finite rotation of a frame in which the material points that are originally along a normal line in the undeformed plate undergo only small displacements. Exact intrinsic virtual strain-displacement relations are derived; using a reduced 2-D strain energy function from which the warping has been systematically eliminated, a set of intrinsic equilibrium equations follows. It is demonstrated that only five equilibrium equations can be derived in this way, because the component of virtual rotation about the normal is not independent. These equations include terms which cannot be obtained without the use of a finite rotation vector which contains three nonzero components. These extra terms correspond to the difference of in-plane shear stress resultants in other theories.
Hodges, Dewey H.↗
Control of elastic robotic systems by nonlinear inversion and modal damping
Energy efficient, lightweight robot arms for space applications have considerable structural flexibility. For large and fast motions, both the nonlinear coupled dynamics and the elastic behavior of the robots must be considered in control system designs. This paper presents an approach to the control of a class of flexible robotic systems. A control law is derived which decouples the joint-angle motion from the flexible motion and asymptotically decomposes the elastic dynamics into two subsystems, representing the transverse vibrations of the elastic link in two orthogonal planes. This decomposition allows the design of an elastic mode stabilizer independently based on lower order models representing structural flexibility. The closed-loop system is shown to be globally asymptotically stable and robust to uncertainty in system parameters. Simulation results are presented to show that large, fast control of joint angles can be performed in spite of space vehicle motion and uncertainty in the payload.
Singh, S. N.↗
Quasistatic vs. Dynamic Modulus Measurements Of Plasma-Sprayed Thermal Barrier Coatings
Plasma-sprayed 8wt% yttria-stabilized zirconia (8YSZ) thermal barrier coatings (TBCs) have been demonstrated to exhibit nonlinear hysteretic elastic behavior by quasistatic cyclic compression and cylindrical punch indentation measurements. In particular, the instantaneous (tangential) elastic modulus increases with applied stress and exhibits significant hysteresis during cycling. Sound velocity (dynamic) measurements also show an increase in TBC modulus with applied compressive stress, but in contrast show no significant hysteresis for the modulus during cycling. The nonlinear elastic behavior of the TBCs evidenced by these tests is attributed to coating compaction and internal sliding. The differences between the quasistatic and dynamic measurements are explained by the relative absence of the effect of internal sliding in the dynamic modulus measurements. By incorporating short load reversals into the larger loading cycle and measuring the instantaneous modulus at the start of each load reversal, the effects of internal sliding can be substantially reduced in the quasistatic measurements, and the resulting modulus values show good agreement with the modulus values determined by dynamic sound velocity measurements.
Eldridge, J. I.↗
Computer program for investigating effects of nonlinear suspension-system elastic properties on parachute inflation loads and motions
A computer program is presented by which the effects of nonlinear suspension-system elastic characteristics on parachute inflation loads and motions can be investigated. A mathematical elastic model of suspension-system geometry is coupled to the planar equations of motion of a general vehicle and canopy. Canopy geometry and aerodynamic drag characteristics and suspension-system elastic properties are tabular inputs. The equations of motion are numerically integrated by use of an equivalent fifth-order Runge-Kutta technique.
Poole, L. R.↗
Nonlinear Curvature Expressions for Combined Flapwise Bending, Chordwise Bending, Torsion and Extension of Twisted Rotor Blades
The nonlinear curvature expressions for a twisted rotor blade or a beam undergoing transverse bending in two planes, torsion, and extension were developed. The curvature expressions were obtained using simple geometric considerations. The expressions were first developed in a general manner using the geometrical nonlinear theory of elasticity. These general nonlinear expressions were then systematically reduced to four levels of approximation by imposing various simplifying assumptions, and in each of these levels the second degree nonlinear expressions were given. The assumptions were carefully stated and their implications with respect to the nonlinear theory of elasticity as applied to beams were pointed out. The transformation matrices between the deformed and undeformed blade-fixed coordinates, which were needed in the development of the curvature expressions, were also given for three of the levels of approximation. The present curvature expressions and transformation matrices were compared with corresponding expressions existing in the literature.
Kvaternik, R. G.↗
Crystalline structure and symmetry dependence of acoustic nonlinearity parameters
A quantitative measure of elastic wave nonlinearity in crystals is provided by the acoustic nonlinearity parameters. The nonlinearity parameters are defined for arbitrary propagation modes for solids of arbitrary crystalline symmetry and are determined along the pure mode propagation directions for 33 crystals of cubic symmetry from data reported in the literature. The magnitudes of the nonlinearity parameters are found to exhibit a strong dependence on the crystalline structure and symmetries associated with the modal direction in the solid. Calculations based on the Born-Mayer potential for crystals having a dominant repulsive contribution to the elastic constants from the interatomic pair potential suggest that the origin of the structure dependence is associated with the shape rather than the strength of the potential. Considerations based on variations in crystal symmetry during loading along pure mode propagation directions of face-centered-cubic solids provide a qualitative explanation for the dependence of the acoustic nonlinearity parameters on modal direction.
Cantrell, John H.↗
Dynamics and stability of elastic Cosserat curves
Nonlinear dynamic theory describing elastic Cosserat curves plane motion, developing linear displacement equations and dynamic stability concept
Desilva, C. N.↗
Finite element methods for nonlinear elastostatic problems in rubber elasticity
A number of finite element methods for the analysis of nonlinear problems in rubber elasticity are outlined. Several different finite element schemes are discussed. These include the augmented Lagrangian method, continuation or incremental loading methods, and associated Riks-type methods which have the capability of incorporating limit point behavior and bifurcations. Algorithms for the analysis of limit point behavior and bifurcations are described and the results of several numerical experiments are presented. In addition, a brief survey of some recent work on modelling contact and friction in elasticity problems is given. These results pertain to the use of new nonlocal and nonlinear friction laws.
Oden, J. T.↗
Mechanics of composite materials: Recent advances; Proceedings of the Symposium, Virginia Polytechnic Institute and State University, Blacksburg, VA, August 16-19, 1982
The present conference on the mechanics of composites discusses microstructure's influence on particulate and short fiber composites' thermoelastic and transport properties, the elastoplastic deformation of composites, constitutive equations for viscoplastic composites, the plasticity and fatigue of metal matrix composites, laminate damping mechanisms, the micromechanical modeling of Kevlar/epoxy composites' time-dependent failure, the variational characterization of waves in composites, and computational methods for eigenvalue problems in composite design. Also discussed are the elastic response of laminates, elastic coupling nonlinear effects in unsymmetrical laminates, elasticity solutions for laminate problems having stress singularities, the mechanics of bimodular composite structures, the optimization of laminated plates and shells, NDE for laminates, the role of matrix cracking in the continuum constitutive behavior of a damaged composite ply, and the energy release rates of various microcracks in short fiber composites.
Hashin, Z.↗
Nonlinear attitude control of elastic spacecraft-antenna system
An approach to large angle rotational maneuvers of a spacecraft-beam-tip body (an antenna or a reflector) configuration based on nonlinear invertibility and linear feedback stabilization is presented. A control law u sub d is derived to obtain independent decoupled control of attitude angles, lateral elastic deflections, slopes due to bending and angular deflection due to torsion at the tip of the beam using torquers and force actuators. For the stabilization of the elastic oscillations, a linear feedback control law, u sub s, is obtained based on a linearized model about the terminal state augmented with a servo-compensator. Simulation results obtained for single axis control, for simplicity, show that large slewing and elastic mode stabilization can be accomplished in spite of uncertainty in the system using the total control u = u sub d + u sub s.
Singh, S. N.↗
Evaluating Novel Polymer-Composite Resins for the Ability to Derive Elastic Properties for Explicit Formulations, or to Develop Nonlinear Models Thereof
This project evaluates the ability to derive elastic material properties for novel additively manufactured carbon-polymer matrix materials. Initially stress-strain equilibrium equations were thought to be sufficient to characterize the elastic region of material performance. However, initial test data shows the cured material behaves nonlinearly in the elastic region. To properly determine the elastic performance, additional strain data must be collected in future testing. This paper discusses the initial test data, methods and models used to describe nonlinear elasticity, and the determination of mean elastic material properties, such as Lame’s constants, using the stress-strain equilibrium equations.
36 MATERIALS SCIENCE↗
Nonlinear Equations of Equilibrium for Elastic Helicopter or Wind Turbine Blades Undergoing Moderate Deformation
A set of nonlinear equations of equilibrium for an elastic wind turbine or helicopter blades are presented. These equations are derived for the case of small strains and moderate rotations (slopes). The derivation includes several assumptions which are carefully stated. For the convenience of potential users the equations are developed with respect to two different systems of coordinates, the undeformed and the deformed coordinates of the blade. Furthermore, the loads acting on the blade are given in a general form so as to make them suitable for a variety of applications. The equations obtained in the study are compared with those obtained in previous studies.
Rosen, A.↗