Showing papers on "Timoshenko beam theory published in 1989"
TL;DR: A technique is presented and experimentally validated for solving the inverse dynamics and kinematics of multi-link flexible robots and shows the potential use of this method not only for open-loop control, but also for incorporation in feedback control strate gies.
Abstract: A technique is presented and experimentally validated for solving the inverse dynamics and kinematics of multi-link flexible robots. The proposed method finds the joint torques necessary to produce a specified end-effector motion. Since the inverse dynamic problem in elastic manipulators is closely coupled to the inverse kinematic problem, the solution of the first also renders the displacements and rotations at any point of the manipulator, including the joints. Further more the formulation is complete in the sense that it includes all the nonlinear terms due to the large rotation of the links. The Timoshenko beam theory is used to model the elastic characteristics, and the resulting equations of motion are discretized using the finite element method. An iterative solu tion scheme is proposed that relies on local linearization of the problem. The solution of each linearization is carried out in the frequency domain.The performance and capabilities of this technique are tested, first through simulation an...
222 citations
TL;DR: In this article, an experimental methodology is presented for the simutaneous determination of the section flexural modulus and the section shear modulus of thin-walled fiber reinforced polyester and vinylester pultruded beams.
Abstract: An experimental methodology is presented for the simutaneous determination of the section flexural modulus and the section shear modulus of thin-walled fiber reinforced polyester and vinylester pultruded beams. A pilot test program, involving four different fiber reinforced plastic (FRP) beams, is described and results are discussed. A slenderness ratio is introduced to characterize the shape of the thin-walled beam, and recommended values of this ratio are suggested for design purposes. With available values of the section moduli the designer has the option of using the Timoshenko beam theory instead of the Euler-Bernoulli beam theory.
114 citations
01 Jan 1989
TL;DR: In this article, the authors present fracture mechanics and experimental mechanics approaches used to characterize mode-II interlaminar fracture of composites, including shear deformation beam and higher-order beam theory.
Abstract: This chapter will present fracture mechanics and experimental mechanics approaches used to characterize mode-II interlaminar fracture of composites. This chapter is organized into four major sections: background, analytical, numerical, and experimental results. The first section documents from an historical viewpoint, the various mode-II specimen geometries that have been proposed prior to the emergence of the end notch flexure (ENF) specimen as the most frequently used test method to characterize mode-II interlaminar fracture toughness. The second section focuses on analytical approaches to model the ENF specimen that includes shear deformation beam theory, shear deformation plate theory where the crack-tip singularity is introduced as a surface traction and a higher-order beam theory. Specimen design procedures to maintain linear elastic response and to minimize geometric non-linearities and friction between crack surfaces are presented. The third section reviews numerical results. Compliance, strain energy release rates, delamination offset from the mid-plane and frictional effects are investigated. Results are compared to analytical solutions. The last section reviews experimental mechanics techniques used to characterize the static mode-II interlaminar fracture toughness of composites.
107 citations
TL;DR: In this paper, a simple one-dimensional finite element was developed for the nonlinear analysis of symmetrically and unsymmetrically laminated composite beams including shear deformation.
Abstract: The purpose of this study was to develop a simple one-dimensional finite element for the nonlinear analysis of symmetrically and unsymmetrically laminated composite beams including shear deformation. The beam element has 10 degrees of freedom at each of the two nodes: the axial displacement, the transverse deflection and the slope due to bending and shear, the twisting angle, the in-plane shear rotation, and their derivatives. The formulation, the solution procedure, and the computer program have been evaluated by solving a series of examples on the static response, free vibration, and nonlinear vibrations of isotropic and laminated beams. For unsymmetrically laminated beams, the nonlinear vibrations were found to have a soft spring behavior for certain boundary conditions as opposed to a hard spring behavior observed in isotropic and symmetrically laminated beams. The in-plane boundary conditions were found to have a significant effect on nonlinear responses.
86 citations
TL;DR: In this article, the main features of contact problems of elastic beams are explored by considering a specific equilibrium problem of a beam in contact with a smooth rigid flat surface, and solutions of four separate linear theories, namely a general theory (G) and three others which are constructed as constrained theories are considered.
60 citations
TL;DR: In this article, a closed-form solution was derived for the displacement and velocity space-time correlation function of the Bresse-Timoshenko beam with transverse damping, generalizing the corresponding result by Eringen for the classical Bernoulli-Euler beam.
50 citations
TL;DR: In this article, a transient thermal stress analysis of a laminated beam made of different materials in multilayers is presented, where the heat conduction problem is treated as a one-dimensional case in the direction of thickness and the transient temperature solution using the Laplace transform method.
Abstract: This paper concerns a transient thermal stress analysis of a laminated beam made of different materials in multilayers. To simplify the problem, we treat the heat conduction problem as a one-dimensional case in the direction of thickness; then we evaluate the transient temperature solution using the Laplace transform method. For the thermoelastic fields, we obtain the thermal stress distributions by using the elementary beam theory and Airy's thermal stress function method. As an example, we carry out numerical calculations for a laminated beam made of five layers and then examine the numerical results.
48 citations
TL;DR: In this article, a study of the growth of delamination due to bending in a [905/05/905] graphite/epoxy laminate is presented, where a plane strain finite element analysis is used to determine the strain energy release rate during delamination in a three-point-bend specimen.
48 citations
TL;DR: In this paper, the authors proposed a theory for sandwich beams with relatively thick facings and moderately stiff cores of either bimodular material (which has different elastic moduli in tension and compression) or ordinary materials and compared it with the classical sandwich theory, which is shown to be unconservative in its predictions of both deflections and maximum shear stresses.
42 citations
TL;DR: In this paper, a finite element for the analysis of thin-walled open section beam structures is presented, which is based on Vlasov's beam theory and does not require the use of numerical integration.
36 citations
Journal Article•
TL;DR: In this article, a method for predicting the slamming load, using strip theory to determine relative motion between the ship and waves, and the rate of change in the momentum of the fluid to calculate the impact force is presented.
Abstract: A ship navigating heavy seas is subjected to wave impacts on its forward and bottom sections These loads induce a transient vibratory response in the hull, which behaves like a free beam interacting with the water This article presents a method for predicting the slamming load, using strip theory to determine relative motion between the ship and waves, and the rate of change in the momentum of the fluid to calculate the impact force The hydrodynamic coefficients are calculated with two-dimensional singularity functions Hull vibratory response is modeled with two- dimensional Timoshenko beam finite elements with a consistent mass formulation used to determine mode shapes and natural frequencies The response is obtained using a Newmark integration scheme Lastly, sample calculations for a cargo ship are presented
TL;DR: In this article, the sensitivity properties of structural models pertinent to robust control system design are investigated, and the applicability of different structural models is also carried out, including Euler-Bernoulli theory and Timoshenko beam theory.
Abstract: This paper investigates sensitivity properties of structural models pertinent to robust control system design. Special emphasis is put on noncollocated systems. Sensitivity analysis to parameter variations and boundary conditions is performed on a representative example of a pinned-free beam with end-point mass and inertia and sensors distributed along the beam. The analysis utilizes a transfer matrix representation, which provides a convenient form for demonstrating the sensitivity of zeros and poles to sensors locations and system parameters. Investigation of the applicability of different structural models is also carried out. Comparison of the Euler-Bernoulli theory and Timoshenko beam theory is discussed and the range of parameters for which each theory is applicable is demonstrated.
TL;DR: In this paper, the bending stiffness and natural frequencies of several shaft geometries with stepped diameter changes are compared using several modelling assumptions, including transfer matrix and finite element approaches, and available experimental data.
TL;DR: In this article, the dynamic and flexural behavior of a rotating sandwich beam with two nonsymmetrical facings is investigated by solving the governing equation using the finite-difference technique.
Abstract: Governing equations for the dynamic and flexural behavior of a rotating sandwich tapered beam with two nonsymmetrical facings are formulated by using the variational principle. Because of the asymmetric geometry and the centrifugal effects, the neutral axis does not necessarily coincide with the centroidal axis. The analysis takes this behavior into consideration and, therefore, differs from existing formulations substantially. Both the core and facings are consistently modeled as either Timoshenko beams or Euler-Bernoulli beams. The flexural behavior of tapered sandwich rotating beams with uniformly or linearly distributed loads is investigated by solving the governing equation using the finite-difference technique.
TL;DR: In this article, a more accurate representation of the dynamic behavior of a beam than conventional beam theory is presented, using the natural vibrations of simply-supported aluminum beams of rectangular cross-sections.
Abstract: Studies making use of higher vibration modes and frequencies have indicated a need for a more accurate beam theory Equations of motion are developed here that give a more accurate representation of the dynamic behavior of a beam than conventional beam theory Results are obtained using these equations for the natural vibrations of simply-supported aluminum beams of rectangular cross-sections These results are compared to results from conventional beam theory, and they are examined to identify where various effects are important
TL;DR: In this article, the 3D elasticity solution of flexure and torsion in adhesive-bonded multilayered beams of uniform cross-section having one end fixed and the other end loaded by transverse forces was reported.
Abstract: A study is reported of the 3-dimensional elasticity solution of flexure and torsion in adhesive-bonded multilayered beams of uniform cross section having one end fixed and the other end loaded by transverse forces. The study found that the elementary beam theory (Beer and Johnston 1981) based on the assumption that plane sections of the beam remain plane after deformation yields an exact elasticity solution for the normal stress for multilayered beams if certain conditions are satisfied. These and other findings are discussed.
TL;DR: In this article, the wave propagation in a split beam is analyzed by treating each section separately as a waveguide and imposing appropriate connectivities at their joints, while the justification of the connectivities is sought through the exact solution of an analogous two-dimensional static problem.
TL;DR: In this paper, a Vlasov type thin-walled beam theory with the effects of flexural-torsional coupling, transverse shear deformation and rotary inertia included is developed for the free vibration analysis of curved thinwalled beams with arbitrary open cross section.
TL;DR: In this article, a high order Timoshenko beam finite element is derived and shown to be very efficient in solving dynamic problems of beam-like truss structures in which the extensional, flexural and shear deformations are coupled.
TL;DR: In this paper, an approximate Green's function for surface displacements in an orthotropic beam is derived as the superposition of the half-plane solution for displacements and the beam theory deflections.
TL;DR: In this paper, a higher-order shear deformation beam theory is presented to analyze geometrically nonliner bending of thick, rectangular beams made from bimodular materials.
TL;DR: In this paper, a beam theory for flexural vibration of thin-walled or solid girders, valid in the higher-frequency domain, is presented by introducing the concept of effective stiffness and mass parameters.
TL;DR: In this article, the authors derived formulas for the stresses and displacements in a bimaterial strip which is subjected to a temperature gradient that varies linearly in the longitudinal direction.
Abstract: Formulas are derived for the stresses and displacements in a bimaterial strip which is subjected to a temperature gradient that varies linearly in the longitudinal direction. The solution is obtained by superposing certain fundamental linear elastic stress states which are compatible with bar and beam theory. The analytical results are approximate in the sense that stress-free boundary conditions are not satisfied exactly, since only zero resultant force and moment conditions are enforced. Finite element calculations have been performed to verify the results and to ascertain the level of stress concentration near the ends of the strip.
TL;DR: A generalized beam theory is presented in which deformation and load are determined simultaneously, in order to analyze statically indeterminant problems involving long bones.
TL;DR: In this article, the application of beam theory in the flexural vibration analysis of thin-walled girders is extended for the high-frequency domain by introducing the concept of effective values of beam parameters.
Abstract: The application of beam theory in the flexural vibration analysis of thin-walled girders is extended for the high-frequency domain by introducing the concept of effective values of beam parameters, that is, cross-sectional moment of inertia, shear area, mass, and mass moment of inertia Formulation of these parameters is based on equivalence of deformation energy and inertia work, respectively, for a considered structure and its beam model, resulting in the same values of their natural frequencies The described procedure may also be used for estimating ship hull properties In this way, applicability of the beam theory is extended to ship hull vibration in the propeller frequency range This is very important at the ship design stage when a quick vibration solution as a part of ship optimization is needed