Showing papers on "Bending moment published in 2001"

Effect of membrane bending stiffness on the deformation of capsules in simple shear flow

Abstract: The effect of interfacial bending stiffness on the deformation of liquid capsules enclosed by elastic membranes is discussed and investigated by numerical simulation. Flow-induced deformation causes the development of in-plane elastic tensions and bending moments accompanied by transverse shear tensions due to the non-infinitesimal membrane thickness or to a preferred configuration of an interfacial molecular network. To facilitate the implementation of the interfacial force and torque balance equations involving the hydrodynamic traction exerted on either side of the interface and the interfacial tensions and bending moments developing in the plane of the interface, a formulation in global Cartesian coordinates is developed. The balance equations involve the Cartesian curvature tensor defined in terms of the gradient of the normal vector extended off the plane of the interface in an appropriate fashion. The elastic tensions are related to the surface deformation gradient by constitutive equations derived by previous authors, and the bending moments for membranes whose unstressed shape has uniform curvature, including the sphere and a planar sheet, arise from a constitutive equation that involves the instantaneous Cartesian curvature tensor and the curvature of the resting configuration. A numerical procedure is developed for computing the capsule deformation in Stokes flow based on standard boundary-element methods. Results for spherical and biconcave resting shapes resembling red blood cells illustrate the effect of the bending modulus on the transient and asymptotic capsule deformation and on the membrane tank-treading motion.

Kinematic pile bending during earthquakes: analysis and field measurements

Abstract: The passage of seismic waves through the soil surrounding a pile imposes lateral displacements and curvatures on the pile, thereby generating ‘kinematic’ bending moments even in the absence of a su...

Diagnostic Lamb waves in an integrated piezoelectric sensor/actuator plate: analytical and experimental studies

Abstract: The objective of this study is to model the diagnostic transient waves in an integrated piezoelectric sensor/actuator plate with a view to using it as a first step towards establishing an entire structural health monitoring system and to provide experimental verification of the proposed models. PZT ceramic disks are surface mounted on an aluminum plate acting as both actuators and sensors to generate and collect A0 mode Lamb waves. Mindlin plate theory is adopted to model the propagating waves by taking both transverse shear and rotary inertia effects into account. Actuator and sensor models are both proposed. The interaction between an actuator and the host plate is modeled based on classical lamination theory. The converse piezoelectric effect of the actuator is treated as an equivalent bending moment applied to the host plate. The sensor acts as a capacitor that converts the sensed strain change into a voltage response. An analytical expression for the sensor output voltage in terms of the given input excitation signal is derived, and then experimental work is performed to verify the accuracy of the analytical model. Experimental results show that single-mode Lamb waves in the plate can be successfully generated and collected through the integrated PZT disks. The experiment also shows that the predicted sensor output for both amplitude and phase agrees well with experimentally collected data.

Is it possible to simulate physiologic loading conditions by applying pure moments? A comparison of in vivo and in vitro load components in an internal fixator.

Abstract: Study design Loads acting in an internal fixator measured in vitro under the application of pure moments such as those commonly used for implant testing and basic research were compared with loads measured in 10 patients in vivo. Objectives To investigate whether these recommended loading conditions are valid by comparing in vivo measurements and those obtained in an in vitro experiment. Summary of background data Pure bending moments are often preferred as loading conditions for spinal in vitro testing, either for implant testing or basic research. The advantage of this loading pattern is that the bending moment is uniform along the multisegmental specimen. However, functional loading of the spine by muscles or external loads subjects the spine to a combination of forces and moments. Methods In an in vivo experiment, loads acting on an internal spinal fixator in 10 patients were determined before and after anterior interbody fusion during flexion, extension, left and right lateral bending, and left and right axial twisting of the upper body with the patient standing. For comparison, an equivalent in vitro data set was created with 7 human lumbar specimens in which the same type of fixator was used. All specimens were tested under the application of pure bending moments in the three main motion planes in the intact state with fixator, after corpectomy, and with bone graft. Results Consistent qualitative agreement between in vivo and in vitro measurements for the loads acting in the internal spinal fixator were found for axial rotation and lateral bending. For flexion and extension, reasonable agreement was found only for the intact spines with fixators. After corpectomy and after inserting a bone graft, the median values for axial force and bending moment in the sagittal plane in vitro did not agree with in vivo measurements. An axial preload in the in vitro experiment slightly increased the axial compression force and flexion bending moment in the fixators. Conclusions The application of pure moments to intact lumbar spinal specimens in vitro produces forces and moments in implants comparable with loads observed in vivo. During basic research on intact specimens or implant testing involving a removed disc or corpectomy, muscle forces are necessary to simulate realistic conditions.

Load transfer approach for laterally loaded piles

Abstract: A two-parameter model has been proposed previously for predicting the response of laterally loaded single piles in homogenous soil. A disadvantage of the model is that at high Poisson's ratio, unreliable results may be obtained. In this paper, a new load transfer approach is developed to simulate the response of laterally loaded single piles embedded in a homogeneous medium, by introducing a rational stress field. The approach can overcome the inherent disadvantage of the two-parameter model, although developed in a similar way. Generalized solutions for a single pile and the surrounding soil under various pile-head and base conditions were established and presented in compact forms. With the solutions, a load transfer factor, correlating the displacements of the pile and the soil, was estimated and expressed as a simple equation. Expressions were developed for the modulus of subgrade reaction for a Winkler model as a unique function of the load transfer factor. Simple expressions were developed for estimating critical pile length, maximum bending moment, and the depth at which the maximum moment occurs. All the newly established solutions and/or expressions, using the load transfer factor, offer satisfactory predictions in comparison with the available, more rigorous numerical approaches. The current solutions are applicable to various boundary conditions, and any pile-soil relative stiffness.

Interfacial stresses in beams and slabs bonded with thin plate

Abstract: A new popular method for retrofitting reinforced concrete beams and slabs is to bond fiber-reinforced plastic (FRP) plates to the soffit. An important failure mode for such strengthened members is the debonding of the FRP plate from the member due to high interfacial stresses near the plate ends. Accurate predictions of the interfacial stresses are a prerequisite for designing against debonding failures. In this paper, a theoretical interfacial stress analysis is presented for simply supported beams and slabs bonded with a thin FRP composite or steel plate and subjected to a uniformly distributed load in combination with a uniform bending moment. The analysis leads to an exact closed-form solution, in which a plane stress model is used for beams and a plane strain model is used for slabs. The salient features of the new analysis include the consideration of nonuniform stress distributions in and the satisfaction of the stress boundary conditions at the ends of the adhesive layer. Numerical results from the present analysis are presented both to demonstrate the advantages of the present solution over existing ones and to illustrate the main characteristics of interfacial stress distributions in beams and slabs.

Dynamic Experiments and Analyses of a Pile-Group-Supported Structure

Abstract: Experimental data on the seismic response of a pile-group-supported structure was obtained through dynamic centrifuge model tests, and then used to evaluate a dynamic beam on a nonlinear Winkler foundation (BNWF) analysis method. The centrifuge tests included a structure supported on a group of nine piles founded in soft clay overlying dense sand. This structure was subjected to nine earthquake events with peak accelerations ranging from 0.02 to 0.7g. The centrifuge tests and dynamic analysis methods are described. Good agreement was obtained between calculated and recorded structural responses, including superstructure acceleration and displacement, pile cap acceleration and displacement, pile bending moment and axial load, and pile cap rotation. Representative examples of recorded and calculated behavior for the structure and soil profile are presented. Sensitivity of the dynamic BNWF analyses to the numerical model parameters and site response calculations are evaluated. These results provide experimental support for the use of dynamic BNWF analysis methods in seismic soil-pile-structure interaction problems involving pile-group systems.

Diagnostic Lamb waves in an integrated piezoelectric sensor/actuator plate - Analytical and experimental studies

Abstract: The objective of this study is to model the diagnostic transient waves in an integrated piezoelectric sensor/actuator plate with a view to using it as a first step towards establishing an entire structural health monitoring system and to provide experimental verification of the proposed models. PZT ceramic disks are surface mounted on an aluminum plate acting as both actuators and sensors to generate and collect A0 mode Lamb waves. Mindlin plate theory is adopted to model the propagating waves by taking both transverse shear and rotary inertia effects into account. Actuator and sensor models are both proposed. The interaction between an actuator and the host plate is modeled based on classical lamination theory. The converse piezoelectric effect of the actuator is treated as an equivalent bending moment applied to the host plate. The sensor acts as a capacitor that converts the sensed strain change into a voltage response. An analytical expression for the sensor output voltage in terms of the given input excitation signal is derived, and then experimental work is performed to verify the accuracy of the analytical model. Experimental results show that single-mode Lamb waves in the plate can be successfully generated and collected through the integrated PZT disks. The experiment also shows that the predicted sensor output for both amplitude and phase agrees well with experimentally collected data.

Flexural–torsional post-buckling analysis of thin-walled elements with open sections

Abstract: The post-buckling analysis of thin-walled elements under compression is investigated. A nonlinear model is developed by using nonlinear relationships between curvatures and bending moments. Warping and shortening effects are considered in the torsion equilibrium equation. Based on Galerkin's method, a nonlinear algebraic system is obtained for simply supported boundary conditions. The three resulting equations in bending and torsion are highly coupled and the Newton–Raphson algorithm with displacement control is adopted for the solution. The post-buckling equilibrium curves are obtained for various sections shapes, such as bisymmetric and monosymmetric sections. The importance of the shortening effect is outlined.

Slip initiation and progression in helical armouring layers of unbonded flexible pipes and its effect on pipe bending behaviour

Abstract: Comparatively straightforward analytical formulations are given for determining the bending moment-curvature relationship for a helical layer in unbonded flexible pipes. The approach takes into account the non-linearity of the layer caused by sliding of individual helical elements between the surrounding layers. Bending stiffness of a helical layer is found to be a function of bending curvature, interlayer friction coefficients and interlayer contact pressures. The analysis presented here is based on the Coulomb friction model and is derived using the principle of virtual work. Theoretical results for a typical unbonded flexible pipe using the non-linear formulation for helical layers are compared with experimental data.

Nonlinear Kinematic Hardening Identification for Anisotropic Sheet Metals With Bending-Unbending Tests

Abstract: An inverse identification technique is proposed based on bending-unbending experiments on anisotropic sheet-metal strips. The initial anisotropy theory of plasticity is extended to include the concept of combined isotropic and nonlinear kinematic hardening. This theory is adopted to characterize the anisotropic hardening due to loading-unloading which occurs in sheet-metals forming processes. To this end, a specific bending-unbending apparatus has been built to provide experimental moment-curvature curves. The constant bending moment applied over the length of the specimen allows one to determine numerically the strain-stress behavior but without Finite Element Analysis. Four constitutive parameters have been identified by an inverse approach performed simultaneously on the bending and tensile tests. Our identification results show that bending-unbending tests are suitable to model quite accurately the constitutive behavior of sheet metals under complex loading paths.

Computerized Method for Preliminary Structural Design of Composite Wind Turbine Blades

Abstract: A computerized method has been developed to aid preliminary design of composite wind turbine blades. The method allows for arbitrary specification of the chord, twist, and airfoil geometry along the blade and an arbitrary number of shear webs. Given the blade external geometry description and its design load distribution, the Fortran code uses ultimate-strength and buckling-resistance criteria to compute the design thickness of load-bearing composite laminates. The code also includes an analysis option to obtain blade properties if a composite laminates schedule is prescribed. These properties include bending stiffness, torsion stiffness, mass, moments of inertia, elastic-axis offset, and center-of-mass offset along the blade. Nonstructural materials-gelcoat, nexus, and bonding adhesive-are also included for computation of mass. This paper describes the assumed structural layout of composite laminates within the blade, the design approach, and the computational process. Finally, an example illustrates the application of the code to the preliminary design of a hypothetical blade and computation of its structural properties.

Effect of membrane bending stiffness on the axisymmetric deformation of capsules in uniaxial extensional flow

Abstract: The effect of interface bending stiffness on the axisymmetric deformation of liquid capsules enclosed by elastic membranes subject to uniaxial extensional flow is considered. Flow-induced deformation causes the development of membrane in-plane elastic tensions and bending moments due to the noninfinitesimal thickness of the membrane or to a preferred equilibrium configuration of an interfacial molecular network, accompanied by transverse shear tensions. The elastic tensions are related to the surface deformation by means of Mooney’s linear constitutive law for thin elastic sheets, and the bending moments are related to the membrane resting shape and to the instantaneous principal curvatures by means of constitutive equations. Interfacial force and torque balances are used to relate the jump in hydrodynamic traction across the interface to the elastic tensions and bending moments. A numerical procedure is implemented for simulating the capsule deformation in uniaxial extensional Stokes flow based on a boundary-integral method. Results on the transient and asymptotic deformation for capsules with spherical unstressed shapes illustrate the effect of bending stiffness expressed by an interface modulus of bending for a broad range of elasticity capillary numbers. It is shown that bending stiffness, however large, is not able to restrain continued deformation beyond a critical capillary number, and its main effect is to cause highly deformed capsules with pointed shapes to develop instead nearly cylindrical shapes with rounded caps.

Active shape control of composite blades using shape memory actuation

Abstract: This paper presents active shape control of composite beams using shape memory actuation. Shape memory alloy (SMA) bender elements trained to memorize bending shape were used to induce bending and twisting deformations in composite beams. Bending-torsion coupled graphite-epoxy and kevlar-epoxy composite beams with Teflon inserts were manufactured using an autoclave-molding technique. Teflon inserts were replaced by trained SMA bender elements. Composite beams with SMA bender elements were activated by heating these using electrical resistive heating and the bending and twisting deformations of the beams were measured using a mirror and laser system. The structural response of the composite beams activated by SMA elements was predicted using the Vlasov theory, where these beams were modeled as open sections with many branches. The bending moment induced by a SMA bender element was calculated from its experimentally determined memorized shape. The bending, torsion, and bending-torsion coupling stiffness coefficients of these beams were obtained using analytical formulation of an open-section composite beam with many branches (Vlasov theory).

Spatial Postbuckling Analysis of Nonsymmetric Thin-Walled Frames. I: Theoretical Considerations Based on Semitangential Property

Abstract: To present the spatial postbuckling analysis procedures of shear deformable thin-walled space frames with nonsymmetric cross sections, theoretical considerations based on the semitangential rotation and the semitangential moment are presented. First, similarity and difference between Rodriguez' rotations and semitangential rotations are addressed. Next, the improved displacement field is introduced using the second-order terms of semitangential rotations and rotational properties of off-axis loads and conservative moments are discussed based on the proposed displacement field. Finally, it is deduced that the resulting potential energy due to stress resultants corresponds to semitangential bending and torsional moments. In a companion paper, the elastic strain energy including bending-torsion coupled terms and shear deformation effects is newly derived and a clearly consistent finite-element procedure is presented based on the updated Lagrangian corotational formulation. Tangent stiffness matrices of the t...

Vibration of pretwisted adaptive rotating blades modeled as anisotropic thin-walled beams

Abstract: Problems related to mathematical modeling and dynamic behavior of pretwisted adaptive rotating blades are considered. The blade is modeled as a thin-wall, single-cell beam encompassing nonclassical effects such as anisotropy, transverse shear, and warping restraint. The adaptive capabilities provided by a system of piezoactuators bonded or embedded into the structure are also implemented in the system. Based on the converse piezoelectric effect and of out-of-phase activation, boundary control moments are piezoelectrically induced at the beam tip. Two feedback control laws relating the induced bending moments with the appropriately selected kinematical response quantities are used, and the beneficial effects of the implementation of the active feedback control, considered in conjunction with that of the structural tailoring on the eigenvibration characteristics, are highlighted.