Free vibration analysis of porous beams with gradually varying mechanical properties

This work is aimed to present analysis on free vibration behavior of porous beams with gradually varying mechanical properties based on a robust finite beam element. The governing equations are developed using a mixed variational formulation considering high-order displacement distribution. A new parabolic distribution of the transverse shear strains is introduced and the zero condition of the shear stresses at the upper and bottom surfaces of the beam is satisfied. The porosity can be spread into the beam with evenly and unevenly distributions. According to a modified power function, the material properties are varying along the thickness direction of the FGM porous beam. The presented results show the effect of gradient index, porosity coefficient and forms, boundary conditions, and geometrical parameters on the vibration of FGM beams. It is found that porous beams can be useful as a passive method for control of vibration for structural components.

Thermal buckling analysis of cross-ply plates based on new displacement field

A higher-order displacement field is used for the analysis of the thermal buckling of composite plates subjected to thermal load; it is based on a constant ‘‘m’’, which is optimized to get results relatively close to those given by 3D elasticity theory. Adequate transverse shear strains distribution through the thickness and free stress surfaces of the plate is satisfied using this theory. Hamilton’s principle is used to derive equations of motion, which are solved using Navier-type series for simply supported plates. Thermal buckling of cross-ply laminates with various (α2 / α1) ratios, number of layers, aspect ratios, E1/E2 ratios, and stacking sequence for thick and thin plates is studied in detail. It is concluded that the obtained results using this displacement field are close to those calculated by 3D elasticity theory and other shear deformation plate theories when m=0.05.

Comparative biomechanics of the Pan and Macaca mandibles during mastication: finite element modelling of loading, deformation and strain regimes

The mechanical behaviour of the mandibles of Pan and Macaca during mastication was compared using finite element modelling. Muscle forces were calculated using species-specific measures of physiological cross-sectional area and scaled using electromyographic estimates of muscle recruitment in Macaca . Loading regimes were compared using moments acting on the mandible and strain regimes were qualitatively compared using maps of principal, shear and axial strains. The enlarged and more vertically oriented temporalis and superficial masseter muscles of Pan result in larger sagittal and transverse bending moments on both working and balancing sides, and larger anteroposterior twisting moments on the working side. The mandible of Pan experiences higher principal strain magnitudes in the ramus and mandibular prominence, higher transverse shear strains in the top of the symphyseal region and working-side corpus, and a predominance of sagittal bending-related strains in the balancing-side mandible. This study lays the foundation for a broader comparative study of Hominidae mandibular mechanics in extant and fossil hominids using finite element modelling. Pan 's larger and more vertical masseter and temporalis may make it a more suitable model for hominid mandibular biomechanics than Macaca .

Stability Analysis of Shear Deformable Trapezoidal Composite Plates

The stability characteristics of shear deformable trapezoidal composite plates are studied here. Thestrain smoothing technique is employed to approximate the membrane strains and curvatures of the edge-based smoothing cells. The transverse shear strains within the Reissner–Mindlin quadrilateral element are obtained using the edge-consistent interpolation approach. At the beginning, the performance of the present numerical technique is examined for the buckling analysis of trapezoidal panels under in-plane compressive or shear stresses. Thereafter, new results on the buckling and postbuckling behaviors of trapezoidal composite plates are presented, for which comparable numerical results are rare in the literature. Representative numerical results are presented to highlight the interaction between the higher pre-buckling stresses and increased stiffness near the shorter edge with fiber orientation and loading direction on the buckling resistance of trapezoidal panels.

An Efficient Beam Element Based on Quasi-3D Theory for Static Bending Analysis of Functionally Graded Beams

In this paper, a 2-node beam element is developed based on Quasi-3D beam theory and mixed formulation for static bending of functionally graded (FG) beams. The transverse shear strains and stresses of the proposed beam element are parabolic distributions through the thickness of the beam and the transverse shear stresses on the top and bottom surfaces of the beam vanish. The proposed beam element is free of shear-looking without selective or reduced integration. The material properties of the functionally graded beam are assumed to vary according to the power-law index of the volume fraction of the constituents through the thickness of the beam. The numerical results of this study are compared with published results to illustrate the accuracy and convenience rate of the new beam element. The influence of some parametrics on the bending behavior of FGM beams is investigated.

Simulating of Bird Strike on Aircraft Laminated Glazing

A bird strike is a critical problem in the context of safety in the aviation industry. All modern aircraft structures are designed with account of likely collision with birds. Thus, aviation standards in force require that the aircraft construction would allow the crew to conclude the flight safely after collision with a 1.81-kg bird. A method for analysing the stress-strained state of laminated airplane glazing at different operational factors is presented. The method includes a technique for strength analysis of the laminated airplane glazing at bird impact, and a technique for analysis of excess pressure. The model of laminated glazing is based on the refined first-order theory accounting for transverse shear strains, thickness reduction and normal element rotation inertia in each layer. The mathematical model of the pressure impulse authentically reproducing the bird impact is based on experimental research. Theoretical results are in good agreement with experimental data, thus allowing to recommend the method to develop new airplane glazing elements.