Horizontally curved isoparametric beam element with or without elastic foundation including effect of shear deformation

A new horizontally curved three-noded isoparametric beam element with or without an elastic base throughout its length, is formulated, in which the same set of parabolic shape functions in natural coordinates is used to interpolate beam geometry as well as displacements at any point of the beam. The formulation includes shear deformation effects and is also capable of accounting for torsional loading. The elastic base is assumed to offer distributed vertical reaction and torque at any point of the beam proportional to the vertical deflection and angle of twist respectively at that point. Development of the stiffness matrix is presented. A two point Gaussian quadrature rule has been followed for the necessary numerical integration. Numerical results for a few sample problems have been presented and comparison with the analytical solutions indicates the suitability of the element.     

Topology optimization of beam cross-section considering warping deformation

The beam cross-section optimization problems have been very important as beams are widely used as efficient load-carrying structural components. Most of the earlier investigations focus on the dimension and shape optimization or on the topology optimization along the axial direction. An important problem in beam section design is to find the location and direction of stiffeners, for the introduction of a stiffener in a closed beam section may result in a topologically different configuration from the original; the existing section shape optimization theory cannot be used. The purpose of this paper is to formulate a section topology optimization technique based on an anisotropic beam theory considering warping of sections and coupling among deformations. The formulation and corresponding solving method for the topology optimization of beam cross-sections are proposed. In formulating the topology optimization problem, the minimum averaged compliance of the beam is taken as objective, and the material density of every element is used as design variable. The schemes to determine the rigidity matrix of the cross-sections and the sensitivity analysis are presented. Several kinds of topologies of the cross-section under different load conditions are given, and the effect of load condition on the optimum topology is analyzed.     

Finite element micromechanical analysis of a unidirectional composite including longitudinal shear loading

A two-dimensional finite element analysis has been extended to include longitudinal shear loadings in the third direction, thus permitting a more complete micromechanical analysis of a unidirectional composite material subjected to combined loading states. The numerical analysis includes temperature and moisture loadings as well as mechanical loadings, and models temperature—and moisture—dependent material properties, into the inelastic range to first failure. Correlations of the predictions of composite material response with available experimental data indicate good agreement.     

Identification and elimination of parasitic shear in a laminated composite beam finite element

A displacement-based finite element for the analysis of laminated composite beams is formulated using strain gradient notation. The definition of the beam’s longitudinal displacement possesses only the independent term (axial displacement) and a term which is linear in the thickness coordinate z. Thus, the finite element is first-order shear deformable. As strain gradient notation is physically interpretable, the contents of the coefficients of the polynomial expansions are identified a priori. Thus, the modeling capabilities as well as modeling deficiencies of the element are identified during the formulation procedure. A single parasitic shear term (spurious) is found to be present in the transverse shear strain expression of the element, which is responsible for locking. This parasitic shear term is also found to be the cause of a qualitative error existing in the representation of transverse shear strain along the length of a typical beam model. As the spurious term has been clearly identified, it can easily be removed to correct the element. The effectiveness of the procedure is shown through numerical analyses performed using the element containing the spurious term and then corrected for it. The beam model is validated by comparing numerical solutions with analytical solutions provided by the minimization of the total potential energy for a given laminated composite beam.     

Real-time rendering of 3-D scenes using subband 3-D warping

Three techniques for increasing the frame rates of three-dimensional warping, namely subsampling, wavelet baseband, and wavelet transform (including high frequencies) are presented. Additionally noninteger and integer splats are applied for the techniques. The Haar baseband and subsampling methods using integer splats both produce excellent frame rates and perceptual quality of warped images.     

A finite element analysis of beams on elastic foundation including shear and axial effects

A displacement finite element method for analyzing a beam on continuous elastic foundation is presented. A three-dimensional model which accounts for the effects of both the Filonenko-Borodich and Pasternak foundation models in a consistent and complete way is used. A variational principle is introduced with the slope field due to bending only and the displacement field approximated by independent quantities subjected to variation. Numerical examples illustrate the accuracy of the element, the importance of shear, axial and shear-axial interaction effects associated with continuous elastic foundation, and finally the application of the element to a rotor supported by two hydrodynamic journal bearings.     

A simple selectively integrated torsion—Flexure coupled tapered beam element with transverse shear deformation

A tapered beam element with torsional flexibility and transverse shear deformation is developed for use in swept plate studies. Recently established guidelines for selective reduced integration allow the use of independent interpolation functions for the transverse deflection $\text{w}$, rotation ψ and torsional rotation θ to obtain an element that does not lock in extremely thin situations encountered in thin beam/plate analysis. The element is tested for free vibration and for the static case of a severely swept cantilever plate of high aspect-ratio subjected to uniform distributed load. The results indicate very good performance of the element.     

Buckling of laminated anisotropic shells including transverse shear deformation

The subspace iteration method used in the buckling options of the shell code FASOR is discussed. Buckling modes of a laminated anisotropic cylindrical shell and a sandwich spherical cap are presented and compared with previously published results.     

Optimization of anisotropic composite panels with T-shaped stiffeners including transverse shear effects and out-of-plane loading

A two-step method to optimize anisotropic composite panels with T-shaped stiffeners, including a new formulation of the transverse shear properties and an approximation of the ply contiguity (blocking) constraints as functions of the lamination parameters is provided. At the first step, a representative element of the stiffened panel (superstiffener) is optimized using mathematical programming and lamination parameters subjected to combined loading (in-plane and out-of-plane) under strength (laminate or ply failure), buckling and practical design constraints. Ply blocking constraints are imposed at this step to improve convergence towards practical laminates. At the second step, the actual superstiffener’s laminates are obtained by using a genetic algorithm. Results, for the case considered, show that the inclusion of transverse shear effects has an associated 2.5% mass penalty and that neglecting its effects might invoke earlier buckling failure. In addition, the influence of designing for failure strength at laminate or ply level is assessed.     

Vibration characteristics of a rotating blade with localized damage including the effects of shear deformation and rotary inertia

The flexural vibration characteristics of a uniform rotating bar with localized zones of damage are studied by using a finite element analysis. The effects of shear deformation and rotary inertia have been taken into consideration. The influences of parameters such as the extent, position of damage and rotational speed on the frequencies of oscillation of the blade are discussed. It is observed that the presence of damage has a marked effect on the natural frequencies. A flaw in the beam near the tip of the blade has substantial effects on the frequencies as rotational speed increases. As the rotary inertia and shear deformation parameters increase, the frequencies increase for all damage parameters.     

Analysis of composite plates by trigonometric shear deformation theory and multiquadrics

In this paper we used for the first time a trigonometric shear deformation theory for modelling symmetric composite plates discretized by a meshless method based on global multiquadric radial basis functions. This trigonometric theory uses trigonometric functions through the thickness direction, allowing for zero transverse shear stresses at the top and bottom surfaces of the plate. The results obtained are compared with solutions derived from other models and numerical techniques. The results show that the use of trigonometric shear deformation theory discretized with multiquadrics provides very good solutions for composite and sandwich plates.     

Influence of shear deformation on the design of the stiffest elastic beam

The calculus of elastic beams for maximum stiffness, that can be understood in several diffent manners, has been usually performed in current literature taking into account only bending deformation. In the present paper such calculus has been extended taking into account shear deformation as well and comparing these results with those obtained considering bending deformation only. Finally an estimation of the error made disregarding shear deformation is also obtained. Received November 27, 1998     

An efficient, conforming axisymmetric shell element including transverse shear and rotary inertia

A conforming, two-node conical element is presented incorporating both transverse shear deformation and rotary inertia effects. The success of the formulation is based on the C⁰ continuity shape functions that, in addition to providing full kinematic compatibility, satisfy the interdependent variable interpolation requirement. This requirement points toward a particular dependence of the kinematic variable interpolations which allow for the satisfaction of the Kirchhoff constraint everywhere in the element domain. There exists an internal degree-of-freedom reduction achieved by means of a continuous shear constraint condition. In the derivation of element matrices, Hamilton's principle is invoked with Gaussian quadratures ensuring exact integration throughout. Excellent convergence characteristics and high accuracy results attainable with the element are demonstrated in static and free vibration problems for thin and moderately thick plates and shells.     

Free vibrations of laminated composite plates using second-order shear deformation theory

A complete set of linear equations of the second-order theory of laminated composite plates are obtained. A generalized Levy type solution in conjunction with the state space concept is used to analyze the free vibration behavior of cross-ply and antisymmetric angle-ply laminated plates. Exact fundamental frequencies of cross-ply plate strips are obtained for arbitrary boundary conditions. The exact analytical solutions are obtained for thick and moderately thick plates as well as for thin plates and plate strips. It is shown that the results of the second-order theory are very close to the results of the first-order and third-order theories reported in the literature, and different from those of the classical Kirchhoff’s theory for thick laminates.     

2-D and 3-D numerical modelling of a dynamic resonant shear stress sensor

Despite the importance of wall shear stress measurements in both fundamental and applied fluid dynamic problems, sensors for this application suffer from several shortcomings. A new class of wall shear stress sensor concept that addresses these shortcomings is studied numerically. The properties of a dynamic resonant shear stress sensor are determined using a specially-developed two-dimensional unsteady boundary layer code and a commercially available three-dimensional fluid model. Several characteristics of the sensors are determined using these models including: static sensitivities with and without pressure gradients, sensor design parameter effects. These results indicate that low amplitude, high resonant frequency operation associated with small sensors will have optimum performance. These results also suggest that a MEMS implementation of this sensor should provide the capability of measuring wall shear stress fluctuations in turbulent flows.     

Nonlinear dynamics of angle-ply composite laminated thin plate with third-order shear deformation

An asymptotic perturbation method is presented based on the Fourier expansion and temporal rescaling to investigate the nonlinear oscillations and chaotic dynamics of a simply supported angle-ply composite laminated rectangular thin plate with parametric and external excitations.According to the Reddy's third-order plate theory,the governing equations of motion for the angle-ply composite laminated rectangular thin plate are derived by using the Hamilton's principle.Then,the Galerkin procedure is applied to...     

Optimized element positions for prescribed radar cross section pattern of linear dipole arrays

Approximate closed‐form expression is derived for the scattering from dipole arrays based on the equivalent circuit theory. Then, a method is proposed for synthesis of dipole arrays to produce desired scattering pattern using genetic algorithm (GA). In the synthesis method, the element positions in an array are considered as the optimization parameter and the derived expression is used to evaluate the fitness function of GA. To assess the validity and efficiency of the proposed method, several linear dipole arrays are designed to obtain scattering pattern with low sidelobe level (SLL). A good agreement between the patterns calculated using the expression and simulated by FEKO validates the accuracy of the presented expression. In addition, the numerical results show that the maximum SLL of the scattering pattern is considerably reduced by optimization. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.     

SO dynamic deformation for building of 3-D models

Three-dimensional (3D) modeling based on an ensemble of multilayer self-organizing (SO) neural networks is described. Our objective for 3D modeling is to construct a representation of a 3D object shape from sensed surface points acquired from the object. Current modeling techniques can be classified into two categories: the static and the dynamic approaches, where the former grounded in computational geometry, and the latter rooted in the mechanics of elastic materials. In this paper, a neural-based dynamic modeling approach is presented. The method used is proved to converge and experimental results are shown which support its applicability to real problems.