Vibration and buckling of composite beams using refined shear deformation

Vibration and buckling analysis of composite beams with arbitrary lay-ups using refined shear deformation theory is presented. The theory accounts for the parabolical variation of shear strains through the depth of beam. Three governing equations of motion are derived from the Hamilton’s principle. The resulting coupling is referred to as triply coupled vibration and buckling. A two-noded C1 beam element with five degree-of-freedom per node which accounts for shear deformation effects and all coupling coming from the material anisotropy is developed to solve the problem. Numerical results are obtained for composite beams to investigate effects of fiber orientation and modulus ratio on the natural frequencies, critical buckling loads and corresponding mode shapes

Isogeometric analysis for functionally graded microplates based on modified couple stress theory

Analysis of static bending, free vibration and buckling behaviours of functionally graded microplates is investigated in this study. The main idea is to use the isogeometric analysis in associated with novel four-variable refined plate theory and quasi-3D theory. More importantly, the modified couple stress theory with only one material length scale parameter is employed to effectively capture the size-dependent effects within the microplates. Meanwhile, the quasi-3D theory which is constructed from a novel seventh-order shear deformation refined plate theory with four unknowns is able to consider both shear deformations and thickness stretching effect without requiring shear correction factors. The NURBS-based isogeometric analysis is integrated to exactly describe the geometry and approximately calculate the unknown fields with higher-order derivative and continuity requirements. The convergence and verification show the validity and efficiency of this proposed computational approach in comparison with those existing in the literature. It is further applied to study the static bending, free vibration and buckling responses of rectangular and circular functionally graded microplates with various types of boundary conditions. A number of investigations are also conducted to illustrate the effects of the material length scale, material index, and length-to-thickness ratios on the responses of the microplates.Comment: 57 pages, 14 figures, 18 table

Flexural behaviour of hardwood and softwood beams with mechanically connected GFRP plates

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Efficient machine learning models for prediction of concrete strengths

In this study, an efficient implementation of machine learning models to predict compressive and tensile strengths of high-performance concrete (HPC) is presented. Four predictive algorithms including support vector regression (SVR), multilayer perceptron (MLP), gradient boosting regressor (GBR), and extreme gradient boosting (XGBoost) are employed. The process of hyperparameter tuning is based on random search that results in trained models with better predictive performances. In addition, the missing data is handled by filling with the mean of the available data which allows more information to be used in the training process. The results on two popular datasets of compressive and tensile strengths of high performance concrete show significant improvement of the current approach in terms of both prediction accuracy and computational effort. The comparative studies reveal that, for this particular prediction problem, the trained models based on GBR and XGBoost perform better than those of SVR and MLP

Modelling of the low-impulse blast behaviour of fibre–metal laminates based on different aluminium alloys

A parametric study has been undertaken in order to investigate the influence of the properties of the aluminium alloy on the blast response of fibre–metal laminates (FMLs). The finite element (FE) models have been developed and validated using experimental data from tests on FMLs based on a 2024-O aluminium alloy and a woven glass–fibre/polypropylene composite (GFPP). A vectorized user material subroutine (VUMAT) was employed to define Hashin’s 3D rate-dependant damage constitutive model of the GFPP. Using the validated models, a parametric study has been carried out to investigate the blast resistance of FML panels based on the four aluminium alloys, namely 2024-O, 2024-T3, 6061-T6 and 7075-T6. It has been shown that there is an approximation linear relationship between the dimensionless back face displacement and the dimensionless impulse for all aluminium alloys investigated here. It has also shown that the residual displacement of back surface of the FML panels and the internal debonding are dependent on the yield strength of the aluminium alloy

Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory

Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory is presented. The core of sandwich beam is fully metal or ceramic and skins are composed of a functionally graded material across the depth. Governing equations of motion and boundary conditions are derived from the Hamilton’s principle. Effects of power-law index, span-to-height ratio, core thickness and boundary conditions on the natural frequencies, critical buckling loads and load–frequency curves of sandwich beams are discussed. Numerical results show that the above-mentioned effects play very important role on the vibration and buckling analysis of functionally graded sandwich beams

A size-dependent functionally graded sinusoidal plate model based on a modified couple stress theory

A size-dependent model for bending and free vibration of functionally graded plate is developed based on the modified couple stress theory and sinusoidal shear deformation theory. In the former theory, the small scale effect is taken into consideration, while the effect of shear deformation is accounted for in the latter theory. The equations of motion and boundary conditions are derived from Hamilton’s principle. Analytical solutions for the bending and vibration problems of simply supported plates are obtained. Numerical examples are presented to illustrate the influences of small scale on the responses of functionally graded microplates. The results indicate that the inclusion of small scale effects results in an increase in plate stiffness, and consequently, leads to a reduction of deflection and an increase in frequency. Such small scale effects are significant when the plate thickness is small, but become negligible with increasing plate thickness

Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories

In this paper, various higher-order shear deformation beam theories for bending and free vibration of functionally graded beams are developed. The developed theories account for higher-order variation of transverse shear strain through the depth of the beam, and satisfy the stress-free boundary conditions on the top and bottom surfaces of the beam. A shear correction factor, therefore, is not required. In addition, these theories have strong similarities with Euler–Bernoulli beam theory in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Equations of motion and boundary conditions are derived from Hamilton's principle. Analytical solutions are presented, and the obtained results are compared with the existing solutions to verify the validity of the developed theories. Finally, the influences of power law index and shear deformation on the bending and free vibration responses of functionally graded beams are investigated

A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams

This paper presents a nonlocal sinusoidal shear deformation beam theory for the bending, buckling, and vibration of nanobeams. The present model is capable of capturing both small scale effect and transverse shear deformation effects of nanobeams, and does not require shear correction factors. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion as well as the boundary conditions of the beam are derived using Hamilton’s principle. Analytical solutions for the deflection, buckling load, and natural frequency are presented for a simply supported beam, and the obtained results are compared with those predicted by the nonlocal Timoshenko beam theory. The comparison firmly establishes that the present beam theory can accurately predict the bending, buckling, and vibration responses of short nanobeams where the small scale and transverse shear deformation effects are significant

Axial-flexural coupled vibration and buckling of composite beams using sinusoidal shear deformation theory

A finite element model based on sinusoidal shear deformation theory is developed to study vibration and buckling analysis of composite beams with arbitrary lay-ups. This theory satisfies the zero traction boundary conditions on the top and bottom surfaces of beam without using shear correction factors. Besides, it has strong similarity with Euler–Bernoulli beam theory in some aspects such as governing equations, boundary conditions, and stress resultant expressions. By using Hamilton’s principle, governing equations of motion are derived. A displacement-based one-dimensional finite element model is developed to solve the problem. Numerical results for cross-ply and angle-ply composite beams are obtained as special cases and are compared with other solutions available in the literature. A variety of parametric studies are conducted to demonstrate the effect of fiber orientation and modulus ratio on the natural frequencies, critical buckling loads, and load-frequency curves as well as corresponding mode shapes of composite beams