Haim Abramovich

Dynamic stiffness analysis of laminated beams using a first order shear deformation theory

In this paper the exact vibration frequencies of generally laminated beams are found using a new method, including the effect of rotary inertia and shear deformations. The effect of shear in laminated beams is more significant than in homogenous beams, due to the fact that the ratio of extensional stiffness to the transverse shear stiffness is high. The exact dynamic stiffness matrix is derived, and then any set of boundary conditions including elastic connections, and assembly of members, can be solved as in the classical direct stiffness method for framed structures. The natural frequencies of vibration of a structure are those values of frequency that cause the dynamic stiffness matrix to become singular, and one can find as many frequencies as needed from the same matrix. In the paper several examples are given, and compared with results from the literature.

Dynamic buckling of beams and plates subjected to axial impact

Abstract Analytical studies with the ADINA computer code were performed to determine the Dynamic Load Amplification Factor (DLF) of metal beams and plates subjected to axial in-plane impact compression loading. The results were compared with experimental ones and those yielded by self developed finite differences programs. The influences of initial geometric imperfections, as well as duration of loading on the DLP were evaluated. As anticipated, the DLFs were usually higher than unity. However, in a few cases, in the presence of certain magnitudes of initial geometric imperfection and for loading durations close to the first natural period in bending, DLFs smaller than unity were observed.

Shear deformation and rotary inertia effects of vibrating composite beams

Free vibration of symmetrically laminated composite beams is studied based on Timoshenko type equations. Shear deformation and rotary inertia are included in the analysis, but with the term representing the joint action of these effects omitted in the Timoshenko equations. Detailed analytical analysis is performed for the natural frequencies of laminated beams with different boundary conditions at their ends, with numerical examples being calculated for a hinged-hinged beam.

Surrogate models for optimum design of stiffened composite shells

An optimization procedure is developed for the design of composite stiffened shells subjected to buckling and post-buckling constraints. The optimization method is based on building surrogate models employing the experimental design and response surface methodology. A combined data set consisting of test results of stiffened shells and numerical data obtained by finite element simulation is used for building the surrogate models. These models are used for sensitivity analysis, evaluation of the weight saving parameters and for design optimization of stiffened composite panels under axial compression loading. It was shown that employing the surrogate models satisfactory accuracy can be achieved to describe the post-buckling behavior of the stiffened panels and to use these models in design optimization.

Buckling Behavior of Composite Laminated Stiffened Panels Under Combined Shear-Axial Compression

Experimental results on the behavior of four torsion boxes, each comprising of two stringer stiffened cylindrical graphite-epoxy composite panels that have been subjected to torsion, axial loading and their combinations are reported. The buckling and post buckling behavior of these torsion boxes demonstrated consistent results. Prior to performing the buckling tests, the initial geometric imperfections of the boxes were scanned and recorded. The tests were complemented by finite element calculations, which were performed for each box. These detailed calculations have also assisted in identifying critical regions of the boxes and the boxes were reinforced accordingly to avoid their premature failure. The tests indicated that: the torsion carrying capacity is laminate lay-up dependent; axial compression results were in very good agreement with previous tests performed with single identical panels; and that the boxes have a very high post-buckling carrying capacity.

Consistent Methodology for the Modeling of Piezolaminated Shells

A consistent methodology is developed and presented for the modeling of the static and dynamic response of anisotropic piezolaminated shells with spatially discrete sensors and actuators. The theory on which the methodology is based is general and can be applied to any piezolaminated shell within the confines of the Kirchhoff-Love thin shell theory. The methodology provides effective tools for replacing the piezoelectric induced-strain loading of the structure with an equivalent mechanical loading. Additionally, it yields the governing equations for the static and dynamic structural response to piezoelectric loading. An indexing technique for structural, actuating, and sensing laminae is proposed. Nondimensional coefficients, which illustrate the actuating capability of the piezoactuators, as well as their relative stiffnesses, are used. The general methodology is applied to laminates with one structural lamina with piezoelectric actuators bonded to one or both of its surfaces. The analytical results are compared with results yielded by the ANSYS® finite element program for a rectangular isotropic plate and a cylindrical panel. The plate case was also investigated experimentally. Excellent agreement is demonstrated between the finite element, experimental, and analytical results.

The electromechanical response of multilayered piezoelectric structures

The constitutive equations of multilayered piezoelectric structures are derived in a new form. In this form, the electromechanical coupling is presented as an additional stiffness matrix. This matrix is a true property of the piezoelectric structure and is independent of specific mechanical boundary conditions that may apply to the structure. A novel model of the electromechanical response of such structures is presented. This model accounts for the three-dimensional (3-D) kinematics of the structure deformation. Solution of example problems using the new model shows excellent agreement with full 3-D finite element simulations. These solutions are also compared to the results of previous two-dimensional (2-D) model approximations presented in literature, and the inaccuracies associated with these previous models are discussed.

Influence of predetermined delaminations on buckling and postbuckling behavior of composite sandwich beams

Abstract An investigation was performed to obtain the behavior of composite sandwich beams in the presence of predetermined delaminations, due to disbonding between the faceplate and the less rigid core. An analytical model for predicting buckling and describing the postbuckling behavior of the beam was developed. Griffiths fracture energy release rate model was introduced to predict the stability of the delamination propagation under external loading. Parametric studies over a wide range of damage sizes, and composite facings were carried out to study the effects of these parameters on the overall behavior of the beams, as well as its damage tolerance. The results demonstrate that sandwich construction is very ‘sensitive’ to the presence of predetermined delaminatoins: premature buckling failure occurs at external loads, which are significantly lower than those corresponding to a ‘perfect’ sandwich beam. The limit load is obtained before delamination propagation takes place. In ‘imperfect’ beams with composite faceplates, the layup sequence affects significantly the load carrying capacity of the beam. It was also shown that the proposed model can be used to study the influences of predetermined delaminations in composite beams.

A Self-Sensing Piezolaminated Actuator Model for Shells Using a First Order Shear Deformation Theory

A composite piezolaminated shallow thin shell theory has been developed in which the individual laminae are capable of electromechanical transduction. Utilizing a first order shear deformation approximation and assuming that an electrical field may be applied only across the thickness of a given lamina, the resulting shell theory shows that piezolaminae are capable of exciting and sensing bending, torsion, inplane shearing, and inplane stretching. Piezolaminae are shown to be incapable of exciting and sensing transverse shear unless a three-dimensional electrical field is applied. Inplane shearing and torsion transduction only becomes possible when the dominant rolling axis of a given piezolamina is skewed such as not to coincide with a principal geometric axis. Constitutive relationships are derived which describe how each piezolamina may function simultaneously as both a sensor and an actuator. Two-dimensional piezoelectric field functions are introduced which describe how nonuniformly distributed electromechanical transduction will affect the nature of the applied excitation and acquired measurement. The equations of motion are also given for a shell in which transverse shear deformation is neglected according to Loves first approximation.

Vibration of a uniform cantilever timoshenko beam with translational and rotational springs and with a tip mass

Abstract A uniform cantilever beam carrying a tip mass at its free end, with translational and rotational springs, can be used as a basic model of many practical structures such as a flexible robot arm or an antenna mast. The aim of the study described here is to investigate the influence of rotary inertia and shear deformation on the natural frequencies of a cantilever beam with translational and rotational springs at an arbitrary point along the beam, carrying a tip mass the center of gravity of which does not coincide with the point of attachment. Frequencies were generated as a function of various parameters of the beam.