A beam theory for thin-walled composite beams

A beam theory is presented that is formulated in terms of the in-plane elastic properties of the panels of the cross-section of a thin-walled composite beam. Shear deformation is accounted for by using a suitable form of the Timoshenko beam theory together with a modified form of the shear coefficient. The theory gives both the bending deflection and the shear deflection of a beam loaded by an applied transverse load. Numerical and graphical results obtained from a computer code show the effects of using different composite material systems and lay-ups in the panels of typical beams.     

Improved neural network model for reverse engineering

While conventional engineering transforms engineering concepts into real parts, in reverse engineering real parts are transformed into engineering models. The construction of a surface from three-dimensional (3D) measuring data points is an important problem in reverse engineering. This paper presents a reconstruction method for the sculptured surfaces from the 3D measuring data points. The surface reconstruction scheme is presented based on a neural network. The reconstruction of the existing surfaces is realized by training the network. A series of measuring points from existing sculptured surfaces is used as a training set. Once the neural network has been trained, it serves as a geometric model to generate all the points that are needed. However, the learning rate for the neural network is relatively slow, and the learning accuracy is often unacceptably low. In this paper, to improve the performance of the neural network, a pre-processor is proposed before the input layer. The pre-processor maps the input into the larger space by generating a set of linearly independent values. The effect of the pre-processor is to increase modelling accuracy, and reduce learning time. Based on this method, experimental results are given to show that the reconstructed surfaces are faithful to the original data points. The proposed scheme is useful for regular or irregular digitized data.     

Reshaping collimated laser beams with Gaussian profile to uniform profiles

A set of holographic filters was developed to convert the Gaussian intensity distribution of a collimated laser beam into a uniform one. The design and the fabricating method of the holographic filters are presented and experimental results are shown.     

Improved model for plate-end shear of CFRP strengthened RC beams

In case of RC members strengthened by means of externally bonded reinforcement, a premature failure can be detected in addition to the conventional modes of failure observed in RC unstrengthened beams. The premature failure occurs mainly due to both shear and normal stresses induced in either the external reinforcement–concrete interface or at the level of steel reinforcement. This research is part of a complete programme aiming to set up design formulae to predict the strength of CFRP strengthened beams, particularly when premature failure through laminates-end shear or concrete cover delamination occurs. Series of RC beams were strengthened with carbon-fiber-reinforced plastic (CFRP) laminates and tested to estimate the extent of the applicability of the formulae proposed by the authors, as well as to study the influence of the layout of the external reinforcement in terms of unsheeted length (the distance between CFRP laminates-end and the nearer support) and cross-sectional area, on the behaviour of strengthened beams. The predictions using the proposed formulae are compared with the obtained experimental results, as well as with the calculated design limit states. The interfacial shear stress and the maximum deflection corresponding to the predicted values at maximum and service loads are also studied.     

An elementary theory of defective beams

Summary Material conservation and balance laws of elementary beam theory have been derived. The application to beams with discontinuities in the stiffness results in a surprisingly simple formula to calculate stress intensity factors of cracked beams.With 6 Figures     

Transformation of gaussian to coherent uniform beams by inverse-gaussian transmittive filters

Several plano-convex aluminum thin films, ~30 nm thick in the center and ~2 mm in diameter, were deposited on microscope cover slides to function as inverse-Gaussian transmittive filters. By placing one of these filters in front of the Gaussian He-Ne laser, we can modify the beam intensity profile in the downstream direction. To yield a uniform beam, the position of the filter must be aligned in the transverse plane for maximum intensity at the output of the filter. These filters are easy to fabricate and are inexpensive. Most important, they can help produce collimated phase-coherent uniform beams, which are useful in high-precision fringe-analysis techniques.     

The refined theory of magnetoelastic rectangular beams

Summary. The problem of deducing a one-dimensional theory from a three-dimensional theory for a soft ferromagnetic elastic isotropic body is investigated. Based on the linear magnetoelasticity, the refined theory of magnetoelastic beams is presented by using the general solution for the soft ferromagnetic elastic solids and the Lure method. Based on the refined theory of magnetoelastic beams, the exact equations and solutions for the homogeneous beams are derived and the equations can be decomposed into three governing differential equations: the fourth-order equation, the transcendental equation and the magnetic equation. Moreover, the approximate equations and solutions for the beam under transverse loadings and magnetic field perturbations are derived directly from the refined beam theory. By omitting higher order terms and coupling effects, the refined beam theory can be degenerated into other well-known elastic and magnetoelastic theoretical models.     

A new approach for elasto-plastic finite strain analysis of cantilever beams subjected to uniform bending moment

The reliability and limits of solutions for static structural analysis depend on the accuracy of the curvature and deflection calculations. Even if the material model is close to the actual material behavior, physically unrealistic deflections or divergence problems are unavoidable in the analysis if an appropriate fundamental kinematic theory is not chosen. Moreover, accurate deflection calculation plays an important role in ultimate strength analysis where in-plane stresses are considered. Therefore, a more powerful method is needed to achieve reliable deflection calculation and modeling. For this purpose, a new advanced step was developed by coupling the elasto-plastic material behavior with precise general planar kinematic analysis. The deflection is generated precisely without making geometric assumptions or using differential equations of the deflection curve. An analytical finite strain solution was derived for an elasto-plastic prismatic/non-prismatic rectangular cross-sectioned beam under a uniform moment distribution. A comparison of the analytical results with those from the Abaqus FEM software package reveals a coherent correlation.     

Improved design of dust test chamber for uniform distribution of dust sedimentation rate

Soiling problems are always encountered for equipment installed in outdoor environments, such as headlamps of automobiles, air conditioners, solar collectors, and so on. How to prevent soiling problems on this equipment is one of the challenges for the design of their external layouts. Thus, evaluations of the dust sedimentation quantities on the surfaces of such equipment are necessary. Outdoor testing is usually straightforward but it takes a long time to experience various environmental parameters, such as dust-laden air, wind speed, wind direction, and so on. Indoor tests, performed in a dust test chamber, are instruments for controlling various environmental parameters independently. The conventional design for a dust test chamber is aimed at providing for a test under extreme environmental conditions. The uniformity of dust sedimentation rate within the chamber is not rigorously controlled. Nevertheless, some applications such as the effect of dust sedimentation on the glazing of solar collector require uniform distribution of dustfall in the test chamber for the indoor (laboratory) test. An improved design for a conventional dust test chamber is proposed. Performance tests done with the remodeled dust test chamber based on the improved design show that the normalized standard deviation of the dustfall concentration can be controlled within 2.41% ± 1.29%.     

The exact theory of one-dimensional quasicrystal deep beams

Without employing ad hoc assumptions, various equations and solutions for quasicrystal beams are deduced systematically and directly from the plane problem of one-dimensional quasicrystals. These equations and solutions can be used to construct the exact theory of deep beams for extension or compression and bending deformation forms. A method for the solution of two-dimensional equations is presented, and with the method the exact theory can now be explicitly established from the general solution of quasicrystals and the Lur’e method. The exact governing equations for beams under transverse loadings are derived directly from the exact beam theory. In three illustrative examples of quasicrystal beams it is shown that the exact or accurate solutions can be obtained by use of the exact theory.     

A higher-order theory for functionally graded beams based on Legendre's polynomial expansion

In this article a higher-order theory for functionally graded beams based on the expansion of the two-dimensional (2D) equations of elasticity for functionally graded materials into Fourier series in terms of Legendre's polynomials is presented. Starting from the 2D equations of elasticity, the stress and strain tensors, displacement, traction, and body force vectors are expanded into Fourier series in terms of Legendre's polynomials in the thickness coordinate. In the same way, the material parameters that describe the functionally graded material properties are also expanded into Fourier series. All equations of the linear elasticity including Hooke's law are transformed into the corresponding equations for the Fourier series expansion coefficients. Then a system of differential equations in terms of the displacements and the boundary conditions for the Fourier series expansion coefficients are obtained. In particular, the first- and second-order approximations of the exact infinite dimensional beam theory are considered in more detail. The obtained boundary-value problems are solved by the finite element method with MATHEMATICA, MATLAB, and COMSOL multiphysics software. Numerical results are presented and discussed.     

Higher-order theory for bending and vibration of beams with circular cross section

This paper presents an efficient and simple higher-order theory for analyzing free vibration of cylindrical beams with circular cross section where the rotary inertia and shear deformation are taken into account simultaneously. Unlike the Timoshenko theory of beams, the present method does not require a shear correction factor. Similar to the Levinson theory for rectangular beams, this new model is a higher-order theory for beams with circular cross section. For transverse flexure of such cylindrical beams, based on the traction-free condition at the circumferential surface of the cylinder, two coupled governing equations for the deflection and rotation angle are first derived and then combined to yield a single governing equation. In the case of no warping of the cross section, our results are exact. A comparison is made of the natural frequencies with those using the Timoshenko and Euler–Bernoulli theories of beams and the finite element method. Our results are useful for precisely understanding the mechanical behavior and engineering design of circular cylindrical beams.     

Free vibration analysis of uniform and stepped cracked beams with circular cross sections

This paper presents a novel numerical technique applicable to analyse the free vibration analysis of uniform and stepped cracked beams with circular cross section. In this approach in which the finite element and component mode synthesis methods are used together, the beam is detached into parts from the crack section. These substructures are joined by using the flexibility matrices taking into account the interaction forces derived by virtue of fracture mechanics theory as the inverse of the compliance matrix found with the appropriate stress intensity factors and strain energy release rate expressions. To reveal the accuracy and effectiveness of the offered method, a number of numerical examples are given for free vibration analysis of beams with transverse non-propagating open cracks. Numerical results showing good agreement with the results of other available studies, address the effects of the location and depth of the cracks on the natural frequencies and mode shapes of the cracked beams. Modal characteristics of a cracked beam can be employed in the crack recognition process. The outcomes of the study verified that presented method is appropriate for the vibration analysis of uniform and stepped cracked beams with circular cross section.     

Improved SHSAW transduction efficiency using grating and uniform electrode guiding

Pure shear-horizontal surface acoustic wave (SHSAW) devices have been increasingly considered for liquidphase and biosensing applications because of their ability to operate under liquid-loaded conditions and intrinsic sensitivity to mass, stiffness, viscosity, and electrical perturbations occurring at the device/fluid interface. Typically, the SHSAW is weakly guided by a free surface boundary condition (BC) or may not even exist for some materials and orientations, such as the quartz ST-90° orientation considered in this work. For a surrounding free surface BC, the interdigital transducer (IDT) typically generates strong shear-horizontal bulk acoustic waves (SHBAWs) relative to SHSAW. For that reason, guiding structures, e.g., dense and/or thick electrodes in periodic or uniform configurations, are incorporated into the design and placed between IDTs in delay-line devices to increase the ratio of transduced SHSAW power to IDT input power, ηSHSAW. The degree of ηSHSAW improvement depends on the thickness, composition, and geometry of the guiding structure. In previous work, the authors evaluated ηSHSAW using hybrid finite and boundary element method (FEM/BEM) models, but were limited to cases of stress-free or finite-thickness-grating surrounding surfaces. This work extends the analysis to the important boundary condition case of uniform finite-thickness electrode guiding, which is typically employed in liquid-phase and biosensor applications. To integrate the uniform electrode guiding structure with the SHSAW device analysis, a combined finite-length uniform electrode structure followed by an additional quarter-wavelength electrode was considered. In this work, it is shown that adjusting the quarter-wavelength electrode's film thickness and length allows cancellation of the SHSAW reflection from the edge discontinuity. As a result, the finite-length uniform guiding electrode can be treated as if it extends to infinity, and ηSHSAW can be easily obtained. In addition, the finite thickness of all electrodes is considered in the calculations. To verify the model, an IDT with uniform guiding electrodes was simulated and compared with the experimental results of a fabricated and tested device. The simulations predict SHSAW excitation directivity of 9 dB by the IDT, which is experimentally confirmed to within 0.8 dB.