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Functionally graded materials (FGMs) are advanced composite materials with spatially varying properties, and their porosity distribution further enhances their complexity. The distribution pattern of porosity within a porous material plays a crucial role in determining the mechanical response of these structures. Therefore, the main objective of this study is to analyze the bending, free vibration, and buckling characteristics of porous FG plates by considering different porosity distributions and their effects on the overall behavior. To achieve this goal, a new finite element model is developed in the framework of an improved first-order shear deformation theory (IFSDT). In contrast to the conventional Mindlin–Reissner theory, the present IFSDT incorporates an improved mathematical formulation and provides a more realistic parabolic depiction of shear strain throughout the plate's thickness without using any shear correction factors. In the present study, five types of porosity distribution functions are considered for the analysis. The material characteristics of the FGM porous plate change gradually in the thickness direction based on a power-law function. The governing equations are derived here using Hamilton's principle, and a finite element method is employed for numerical analysis. Comparative analyses with previously published literature underscore the precision and simplicity of our developed finite element model. Moreover, the effects of various types of loads, porosity parameters, power-law index, side-to-thickness ratio, aspect ratio, porosity distributions and boundary conditions on the deflections, natural frequencies, and critical buckling loads are thoroughly analyzed in detail. Finally, the findings of this research contribute to the understanding of the mechanical behavior of FGMs and pave the way for designing and optimizing novel porous functionally graded structures. [ABSTRACT FROM AUTHOR]

A study based on the transient responses of bio-inspired helicoidal laminated composite plates is performed by using a higher-order finite element model (HOFEM) consisting of the thickness stretching effect. The obtained results show good agreement with those available in the open literature. The shear locking phenomena is not inspected by employing the developed HOFEM for the helicoidal lamination schemes. The effects of path of the concentrated moving load, lamination scheme, boundary condition, speed, aspect and orthotropy ratios on the transient responses are investigated. Dynamic dimensionless center deflections and dynamic amplification factors are affected by considering not only the lamination scheme but also the path of the load, boundary condition, orthotropy and aspect ratios. [ABSTRACT FROM AUTHOR]

Based on doublet mechanics theory and various beam theories, this paper presents free vibration of axially loaded zigzag and armchair nanobeams. A two-noded higher order beam element is used to solve the problems of nanobeams with various boundary conditions. The verification studies in terms of fundamental frequencies and buckling loads are performed by comparing the results by the present model with Molecular Dynamic Simulations, Doublet Mechanics, and Eringen's nonlocal theory. The effects of material length scale parameter, slenderness ratio, nanotube model and boundary conditions on the fundamental frequencies of axially loaded nanobeams are investigated in details. Softening material behavior is detected for zigzag and armchair nanobeams. Having stiffer boundary conditions lead to the effect of material length scale parameter to be observed more prominently. [ABSTRACT FROM AUTHOR]

The mechanical behaviours of bio-inspired helicoidal symmetric laminated composite (BIHLC) beams are investigated via the Ritz method. By exploiting the variational formulation, equations of motion along with element stiffness, geometrical stiffness, and mass matrices are derived. The study conducts a thorough examination, covering bending, buckling stability, and free vibration analyses of BIHLC beams with various lamination schemes. The developed model is verified against existing literature on conventional composite laminated and BIHLC beams. The study also examines the mechanical response of BIHLCs, considering boundary conditions, lamination schemes, orthotropy ratios, and aspect ratios. Notably, deflections, critical buckling loads, and fundamental frequencies demonstrate variations dependent on the specific lamination scheme, boundary condition, and aspect ratio. Novel findings, presented for the first time, offer valuable insights for future studies in this area. [ABSTRACT FROM AUTHOR]

• Higher order FEMs are proposed for bio-inspired laminated composites plates using a quasi-3D theory for the first time. • Three different FEMs are derived based on non-conforming elements with different number of nodes and degree of freedom. • No shear locking phenomenon was observed in the analyses conducted using these FEMs. • Effects of lamination scheme, orthotropy ratio and aspect ratio on the mechanical response of the bio-inspired helicoidal composite plates are examined. A comprehensive study is carried out by employing various finite element models (FEMs) for the bending, buckling stability and free vibration analyses of bio-inspired helicoidal composite plates with various lamination schemes. A higher order quasi-3D kinematic plate theory is developed to include a shear deformation effect. The variational formulation of the problem is exploited to derive the equations of motion, element stiffness, geometrical stiffness, and mass matrices based on a non-conforming rectangular element. Three different finite elements models are derived based on non-conforming elements with different number of nodes and degree of freedom. The developed finite element model has been validated with those found in the open literature. The effects of boundary condition, lamination scheme, orthotropy ratio and aspect ratio on the mechanical response of the bio-inspired helicoidal composite plates are examined. Notably, for the lamination schemes investigated in this study, no shear locking phenomenon was observed in the analyses conducted using these FEMs. Dimensionless centre deflections, critical buckling loads and fundamental frequencies of bio-inspired helicoidal composite plates vary depending on the type of lamination scheme, boundary condition and aspect ratio. The new orientation schemes can replace the traditional ones to overcome the shear singularity and overcome the delamination defects. [ABSTRACT FROM AUTHOR]

Purpose: The study aims to present a new meshless method based on the Taylor series expansion. The compact supported radial basis functions (CSRBFs) are very attractive, can be considered as a numerical tool for the engineering problems and used to obtain the trial solution and its derivatives without differentiating the basis functions for a meshless method. A meshless based on the CSRBF and Taylor series method has been developed for the solutions of engineering problems. Design/methodology/approach: This paper is devoted to present a truly meshless method which is called a radial basis Taylor series method (RBTSM) based on the CSRBFs and Taylor series expansion (TSE). The basis function and its derivatives are obtained without differentiating CSRBFs. Findings: The RBTSM does not involve differentiation of the approximated function. This property allows us to use a wide range of CSRBF and weight functions including the constant one. By using a different number of terms in the TSE, the global convergence properties of the RBTSM can be improved. The global convergence properties are satisfied by the RBTSM. The computed results based on the RBTSM shows excellent agreement with results given in the open literature. The RBTSM can provide satisfactory results even with the problem domains which have curved boundaries and irregularly distributed nodes. Originality/value: The CSRBFs have been widely used for the construction of the basic function in the meshless methods. However, the derivative of the basis function is obtained with the differentiation of the CSRBF. In the RBTSM, the derivatives of the basis function are obtained by using the TSE without differentiating the CSRBF. [ABSTRACT FROM AUTHOR]

• Size-dependent responses of 2D FG porous microbeams are studied using the modified strain gradient theory. • Two different porosity distribution models for 2D FG microbeams are considered. • Material length scale parameter (MLSP) is varied in both the axial and thickness directions as well as porosity. • The effects of small size, MLSP, porosity, gradient indexes and boundary conditions are investigated. • The effect of variable MLSP is significant and should be considered for analysis of 2D FG porous microbeams. Finite elemen model for the structural behaviours of bi-directional (2D) FG porous microbeams based on a quasi-3D theory and the modified strain gradient theory (MSGT) is presented. As the main novelty of this study, in order to capture accurately the size effects, the MSGT is employed with three material length scale parameters (MLSPs) rather than the modifed couple stress theory (MCST) with only one MLSP. The material properties including three MLSPs are varied in both the axial and thickness directions as well as porosity. By using a quasi-3D theory, which inludes normal and shear deformations, the governing equations for static, vibration and buckling analysis are derived and solved by Hermite-cubic beam element for various boundary conditions. Through numerical examples, effects of variable MLSP and porosity as well as gradient index in two directions on the deflections, natural frequencies and buckling loads of 2D FG porous microbeams are examined. [ABSTRACT FROM AUTHOR]

Since the two-directional functionally graded (2D-FG) materials can satisfy the new requirements raised based on the elimination of the stress concentration, delamination and cracking problems accompanying with the low cost and lightweight on the structures without sacrificing the stiffness and strength, the structural analyses of these structures become more important than ever. Moreover, the usage of the micro-electromechanical systems composed of 2D-FG materials has been increasing in automotive, military, space, biomedical, and nuclear energy industries. Within this study, the free vibration and buckling behaviors of 2D-FG porous microbeams are investigated based on the modified couple stress theory by employing a transverse shear-normal deformation beam theory and using finite element method. The effects of the thickness to material length scale parameter (MLSP) accompanying with the micro-porosity volume fraction ratio, boundary condition, aspect ratio, and gradient index on the dimensionless fundamental frequencies and dimensionless critical buckling loads of the 2D-FG porous microbeams are investigated. Moreover, with assumption of the variable material length scale parameters (VMLSP), the computed results are compared with ones obtained by employing constant MLSP. It is found that VMLSP increases the stiffness of the 2D-FG porous microbeams and effects the free vibration and buckling responses of these structures. [ABSTRACT FROM AUTHOR]

In this paper, the free vibration and buckling responses of laminated composite and sandwich microbeams with arbitrary boundary conditions are investigated. The governing equations based on the modified couple stress theory are derived by using the total potential energy of a microbeam and employing a transverse shear-normal deformable beam theory. Extensive analysis results in terms of dimensionless fundamental frequencies and dimensionless critical buckling loads are introduced for various boundary conditions, aspect ratios, orthotropy ratios, fiber orientation angles, thickness to material length scale parameter ratios, and core thickness to face layer thickness ratios. [ABSTRACT FROM AUTHOR]

• Free vibration behavior of rotating 2D-FG porous sandwich microbeams are studied. • A transverse shear-normal deformation beam theory has been developed. • The modified couple stress theory has been used in order to include size effects. • Results can be useful for the design of size dependent rotating porous micro beams. Within this study, the free vibration behavior of rotating two-directional functionally graded porous sandwich microbeams is studied based on the modified couple stress theory by employing a transverse shear-normal deformation beam theory. The effects of the thickness to material length scale parameter accompanying with the porosity volume fraction coefficient, boundary condition, aspect ratio, hub ratio, dimensionless rotation speed and gradient index on the dimensionless fundamental frequencies of the two-directional functionally graded porous sandwich microbeams are investigated. It is found that the dimensionless fundamental frequencies are significantly affected by the variation of the thickness to material length scale parameter, hub ratio, dimensionless rotation speed and porosity volume fraction coefficient. The normal deformation effect is very important especially while the variations of the dimensionless rotation speed, hub ratio and gradient index are considered. Moreover, the mode shapes of the rotating two-directional functionally graded porous sandwich microbeams are also influenced with respect to the variation of the porosity volume fraction coefficient. As a result, the optimum design of the microstructures accompanying with the lightweight and low-cost objectives can be achieved by controlling the material and porosity distribution through the body of the microstructure. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Abstract In this paper, the eigenfrequencies of rotating laminated composite (LC) and sandwich microbeams with different boundary conditions (BCs) are studied. The size-dependent variational formulation of the problem is obtained based on the Modified Couple Stress Theory (MCST) by employing a transverse shear-normal deformable beam theory and finite element method (FEM) formulation. The convergence and verification studies of the developed code are carried out and computed results in terms of dimensionless fundamental frequencies (DFFs) are compared with the available ones in the open literature. Various BCs, aspect ratios, fiber orientation angles, thickness to material length scale parameter (MLSP) ratios, core thickness to face layer thickness ratios, dimensionless rotation speeds (DRSs) and hub ratios are employed for the extensive analyses. It is found that the DFFs of the LC microbeams are highly affected by the small size effect accompanying with the orthotropy ratios, DRSs, hub ratios and fiber orientation angles. The effect of the small size on the DFFs of the rotating clamped-clamped LC microbeams is more pronounced than on those of the rotating clamped-free LC microbeams. The hub ratio has a significant effect on the DFFs of the rotating LC microbeams than the rotation speed. [ABSTRACT FROM AUTHOR]

Abstract This paper is dedicated to study the elastic buckling behavior of isotropic, laminated composite and sandwich beams subjected to various axially varying in-plane loads and boundary conditions (BCs). The formulation of the problem is derived by using the Ritz method with the displacement field based on a shear and normal deformable beam theory (SNDBT). Polynomial functions are employed to present the displacement field. The convergence studies are performed and then obtained results are compared with those of reported works. Results from extensive analysis are presented for different BCs, aspect ratios, orthotropy ratios, fiber angles and loading conditions. It is observed that the type of the axially variable in-plane load significantly affects the critical buckling loads and mode shapes of the beams depending on the BCs. The normal deformation effect depends on not only the aspect ratio but also BCs and the fiber orientation angles. [ABSTRACT FROM AUTHOR]

This paper presents the static behaviour of two-directional functionally graded sandwich beams by using the Euler-Bernoulli, Timoshenko and Reddy-Bickford beam theories and the Symmetric Smoothed Particle Hydrodynamics (SSPH) method. The SSPH code developed based on the present formulation of the functionally graded sandwich beam is validated by solving a simply supported conventional functionally graded beam problem. Numerical results which are in terms of maximum dimensionless transverse deflections, dimensionless axial and transverse shear stresses are compared with the analytical solutions and the results from previous studies. Various FG sandwich beam structures are investigated by considering different beam theories, aspect ratios (L/h) and sets of boundary conditions and using power-law distribution. [ABSTRACT FROM AUTHOR]

In the study, three different higher order finite element models (HOFEMs) are developed to perform the transient analysis of functionally graded (FG) microplates subjected to different dynamic loads, namely, sinusoidally distributed step and exponential blast loads. A normal and shear deformable plate theory with five unknowns is used to present displacement field and modified strain gradient theory is employed for small-scale effect. A rectangular four-noded element and Newmark's method is used to solve transient analysis of FG microplates. The effects of boundary condition, type of dynamic loading, thickness to material length parameter, aspect ratio, gradient index and CPU time are investigated. It is found that two of the HOFEMs developed based on the C1 and C2 continuity requirements produced almost same numerical results. However, the one with 36 unknows per element yields slightly different results than the others. The HOFEM satisfying the C1 continuity requirement consumes the minimum computational time. • Three different higher order finite element models (HOFEMs) are developed. • Transient analysis of FGM microplates is performed by using the MSGT. • Sinusoidally distributed step and sinusoidally distributed exponential blast loads are applied. • A normal and shear deformable plate theory with five unknowns is used. [ABSTRACT FROM AUTHOR]

In the study, the modified strain gradient elasticity theory is used to investigate the transient vibrations of the multi-directional functionally graded square microplates subjected to a moving concentrated load by employing a normal and shear deformable plate theory with five unknowns based on the Newmark's method for the first time. In-plane displacement and thickness stretching component of the transverse displacement are approximated by using a rectangular four-noded element with 16 unknows satisfying C1 continuity requirement. In addition, bending and shear components of the transverse displacement are presented by employing a rectangular four-noded element with 24 unknows called as a higher order finite element model (HOFEM) is developed to analyse the dynamic amplification factors and time history analysis of strain gradient multi-directional functionally graded square microplates. The effects of the boundary condition, thickness to material length parameter, gradient index in three directions, aspect ratio, and dimensionless load velocity parameter are examined. It is exhibited based on the results that dynamic amplification factors and dynamic dimensionless center deflections of multi-directional functionally graded strain gradient microplates are significantly affected by the variation of the analysis parameters provided above. [ABSTRACT FROM AUTHOR]

[Display omitted] • A higher order finite element model is presented based on a Quasi-3D plate theory. • The material properties vary in-plane directions. • Transient analysis of two-directional microplates are performed. • A concentrated moving harmonic load is applied. • Various boundary conditions are considered. This study presents the higher order finite element model to explore the transient vibration of two-dimensional functionally graded (2D-FG) porous microplate under harmonic moving loads, that can be helped in design of nanoplate devices such as NEMS, nanofilters, nanoresonators, and nanoswitches. A normal and shear deformable plate theory with five unknowns is exploited with the modified couple stress theory to portray the kinematic relations, constitutive stress–strain equations, and size-dependence effect. This complicated problem is investigated for the first time based on Newmark's method to obtain time history analysis of 2D-FG porous microplates having in-plane inhomogeneity. In-plane displacements and stretching component of the transverse displacement are interpolated by using Bogner-Fox-Schmit rectangular element with four degrees of freedom (DOF) for each node satisfying the C1 continuity requirement. In addition, bending and shear components of the transverse displacement are presented by a nonconforming rectangular element with six DOF for each node satisfying the C2 continuity requirement. Various boundary conditions are considered to evaluate the influences of the thickness to material length parameter, aspect ratio, gradient index in two directions, material loss due to porosity in two directions, load velocity parameter and load excitation frequency ratio. It is revealed based on the results that dynamic deflections of 2D-FG porous microplates are significantly affected by the variation of the analysis parameters mentioned above. [ABSTRACT FROM AUTHOR]

The Symmetric Smoothed Particle Hydrodynamics (SSPH) method is applied to solve elastostatic deformations of isotropic tapered beams subjected to different sets of boundary conditions. Governing equations are presented by using either the Euler-Bernoulli and Timoshenko beam theories. The performance of the SSPH method is evaluated by using different numbers of nodes in the problem domain and employing different beam theories for the numerical solutions of the iostropic tapered beam problems. To validate the performance of the SSPH method, comparison studies in terms of transverse deflections and axial stresses are carried out with the analytical solutions of Euler Bernoulli Beam Theory. Since there is no available closed form solutions of the problems based on the Timoshenko Beam Theory, the analytical solutions obtained by the Euler Beam Theory are used for the comparison purposes. It is observed that the SSPH method has the conventional convergence properties and yields smaller L2 error. [ABSTRACT FROM AUTHOR]

By using sinusoidal beam theory and doublet mechanics formulation, this paper investigates free vibrations of curved zigzag nanobeams. A finite element doublet mechanics (FEDM) model is developed and corresponding material-length-scale-parameter (MLSP, η FEM) is defined to solve the problems. The proposed model is validated by comparing the results with those from molecular dynamic simulations (MDS), DM and Eringen's nonlocal theory. For armchair single-walled CNTs, it is observed from previous study that while the MLSP of Eringen's nonlocal theory should be calibrated with the variation of length/tube diameter (L / d) for better accuracy with MDS, this value of proposed FEDM does not change. Besides, it does not depend on the boundary conditions unlike the Eringen's nonlocal theory. The effects of MLSP, slenderness ratio, open angle and boundary conditions on the natural frequencies of curved nanobeams are studied. Some new results are represented for benchmark purpose. [ABSTRACT FROM AUTHOR]

Because the proportion between the compressive strength of high‐performance concrete (HPC) and its composition is highly nonlinear, more advanced regression methods are demanded to obtain better results. Super learner models, which are based on several ensemble methods including random forest regression (RFR), an adaptive boosting (AdaBoost), gradient boosting machine (GBM), extreme gradient boosting (XGBoost), light gradient boosting machine (LightGBM), categorical gradient Boosting (CatBoost), are used to solve this complicated problem. A grid search method is employed to determine the best set of hyper‐parameters of each ensemble algorithm. Two super learner models, which combine all six models or select the top three effective ones as the base learners, are then proposed to develop an accurate approach to estimate the compressive strength of HPC. The results on four popular datasets show significant improvement of the proposed super learner models in terms of prediction accuracy. It also reveals that their trained models always perform better than other methods since their errors (MAE, MSE, RMSE) are always much lower and values of R2 are higher than those of the previous studies. The proposed super learner models can be used to provide a reliable tool for mixture design optimization of the HPC. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study on bending, vibration and buckling behaviours of the zigzag and armchair nanobeams. Based on a third order shear deformation beam theory and the doublet mechanics, a finite element model is proposed and employed to solve the problems of zigzag and armchair nanobeams with various boundary conditions for the first time. The verification is performed by comparing the numerical results with those from the previous studies with respect to various boundary conditions. A number of numerical examples on zigzag and armchair nanobeams with four boundary conditions have been carried out. The effects of material length scale parameters, aspect ratio, nanobeam model and boundary conditions on the displacements, natural frequencies and buckling loads of nanobeams are investigated in details. Some new results, which are not available in open literature, are provided as references for the future studies. [Display omitted] • The structural behaviors of the zigzag and armchair nanobeams are presented. • Doublet mechanics and finite element formulation are used. • S–S, C–S, C–C and C–F boundary conditions are analyzed for the first time. [ABSTRACT FROM AUTHOR]

• Structural behaviours of CNTRC and GPLRC beams are studied. • Normal and shear effects are included in the governing equations of motion. • Distribution pattern, volume fraction of CNTs, GPL weight fraction, etc. are investigated. • A finite element model is developed to analyze beams for various boundary conditions. This paper investigates bending, vibration and buckling analysis of carbon nanotube-reinforced composite (CNTRC) and graphene nanoplatelet-reinforced composite (GPLRC) beams. Both normal and shear effects are included in the formulation of the governing equations of motion of the beams. Finite element model is employed to determine displacements, critical buckling loads and natural frequencies of the beams with different boundary conditions. Several important factors in parametric studies including distribution pattern, volume fraction of CNTs, GPL weight fraction, slenderness ratio, boundary condition, etc. are investigated. Some new results are given as benchmark for further validation. [ABSTRACT FROM AUTHOR]

• A CNT distribution model in two directions is proposed. • Free vibration behaviors of 2D-FG CNTRC plates are studied. • Various CNT volume fractions are employed in the analysis. • Third order shear deformation theory with finite element formulation is employed. • The results obtained by using 1D-FG CNTRC and 2D-FG CNTRC models are discussed. The dynamical analysis of two directional functionally graded carbon nanotube reinforced composite (2DFG-CNTRC) plates are studied for various boundary conditions. The effects of the CNT distribution in the two directions on the dimensionless frequencies are investigated and compared with the unidirectional CNT distributions (1DFG-CNTRC) with respect to the variation of the CNT configuration, volume fraction and aspect ratio. Based on the variational formulation, the numerical results are obtained by using a finite element model. It is found that the volume fraction of the CNTs is affected with respect to the y direction and the difference between the dimensionless fundamental frequencies calculated based on the 2DFG-CNTRC and 1DFG-CNTRC configurations is significant. Moreover, for CFFF plates, the difference between the dimensionless frequencies obtained based on the 2DFG-CNTRC and 1DFG-CNTRC configurations is approximately 43.5% and 39% for 5th mode of the "U" and "V" type CNT configurations and 42% for 6th mode of the "X" type CNT configuration while the aspect ratio is set to 50. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study on bending, vibration and buckling behaviours of the multi-directional FG microplates. The material properties vary continuously both in-plane and through-thickness directions. Based on a quasi-3D shear and normal deformation plate theory and the modified strain gradient theory, a finite element model is proposed and employed to solve the problems of the multi-directional FG microplates with various boundary conditions. The verification is performed by comparing the numerical results with those from the previous studies. A number of numerical examples on the multi-directional FG microplates with nine boundary conditions and power-law index have been carried out. The effects of three material length scale parameters, aspect ratio, gradient indexes in spatial directions and boundary conditions on the displacements, natural frequencies and buckling loads of 1D, 2D and 3D-FG microplates are investigated in details. Some new results, which are not available in open literature, are provided as references for the future studies. [ABSTRACT FROM AUTHOR]

In this paper, the size-dependent responses of functionally graded (FG) porous microbeams using a quasi-3D theory and the modified strain gradient theory are investigated. Three different porosity distribution models of the FG porous microbeams are considered. By using the rule of mixture, all material properties including the material length scale parameters (MLSPs) are functions of the thickness, porosity coefficient and gradient index. The size-dependent governing equations are derived, and beam element is used to solve the problems. The verification of the proposed model is carried out and the effects of variable MLSP, porosity coefficient, gradient index and boundary conditions on the structural responses of FG porous microbeams are investigated. It can be observed that the effect of variable MLSP is significant and should be included for an accuracy analysis of the FG porous microbeams. [ABSTRACT FROM AUTHOR]

This work is presented to investigate the structural responses of three directional functionally graded (3D-FG) microplates by using the formulations of the modified couple stress theory (MCST) and finite element method. Their material properties including material length scale parameter (MLSP) are varied in three spatial directions with inclusion of the porosity volume fraction varies through the thickness direction. The governing equations for static, vibration and buckling analysis are derived and solved by conforming element for various boundary conditions. Through numerical examples, effects of variable MLSP and porosity as well as gradient index in spatial directions on the deflections, natural frequencies and buckling loads of 3D-FG porous microplates are examined. [ABSTRACT FROM AUTHOR]

This paper studies the bending, buckling and free vibration analyses of functionally graded (FG) sandwich microbeams using the third-order beam theory. The modified strain gradient theory (MSGT) with three material length scale parameters (MLSPs) is used to capture the size effect. The Mori-Tanaka homogenization scheme is employed to model the material distributions through the thickness. Finite element model is formulated to solve the problems. Verification studies for epoxy and FG microbeams are carried out to validate of the present model. Comparisons of the results of three different models such as MSGT, the modified couple stress theory (MCST) and classical continuum theory (CCT) are presented. Effects of small size, gradient index, shear deformation and boundary conditions on the structural behaviours of microbeams are investigated. Some new results of FG sandwich microbeams for both models (MCST and MSGT) are presented for the first time and can be used as benchmark in future studies. [ABSTRACT FROM AUTHOR]

This study is dedicated to understand the possibility of bending before the bifurcation buckling of the functionally graded (FG) plate which has the unsymmetrical material property distribution according to the its midplane. Based on the midplane formulation, the dimensionless critical buckling loads (DCBLs) of FG plates are computed by using a finite element method and shear and normal deformable plate theory for nine different boundary conditions (CCCC, CCCS, SCSC, SSSC, SSSS, CSCF, SCSF, SSSF and SFSF). And then, the FG plate is subjected to in-plane loads which are less than the associated DCBLs to observe the possibility of bending before buckling. It is found that the bifurcation buckling can only be obtained for CCCC, SCSC and SSSC BCs. The bifurcation buckling is impossible for other boundary conditions. For the FG plates having unsymmetrical design, the DCBLs are numerically calculated based on the neutral surface approach as well. It is noteworthy that the true bifurcation buckling can only be observed by using the neutral surface formulation. The transverse deflection due to the bending is quite pronounced especially for the plates with free edge. Since in-plane load is applied to the free edge, the transverse deflection is inevitable for the FG plates. [ABSTRACT FROM AUTHOR]

The size dependent natural frequencies of functionally graded (FG) shear and normal deformable porous square microplates are investigated within this paper for arbitrary boundary conditions. By utilizing the modified couple stress theory, the finite element model is developed based on a shear and normal deformation plate theory and the variational formulation. The material length scale parameter (MLSP) is taken as variable. The effects of the aspect ratio, gradient index, boundary condition, thickness to MLSP ratio, porosity volume fraction and variable MLSP on the dimensionless natural frequencies are investigated for the FG shear and normal deformable porous square microplates. It is found that the difference between the numerical computations employing the constant and variable material length scale parameters is significant. In addition, it is found that with an increment in the aspect ratio, the effect of the MLSP on the natural frequencies increases, especially for the thick microplates. It can be concluded that for the thick microplates (length / t h i c k n e s s ≤ 10), the effect of the variable MLSP on the natural frequencies with respect to the changing of the thickness to MLSP is more emphasized than the effect obtained by the constant MLSP for all studied boundary conditions. [ABSTRACT FROM AUTHOR]

This paper examines the static and vibration analysis of functionally graded sandwich thin-walled microbeams using the modified couple stress theory. The material properties in both web and flanges vary continuously through their thickness. The equations of motion are derived and solved by the Ritz method. Verification studies are performed on the bending and vibration responses of FG sandwich thin-walled beams. The effects of material distribution, span-to-height's ratio, and material length scale parameters on the responses of microbeams for various boundary conditions are investigated. The results of the analysis indicate that the deflections and natural frequencies of functionally graded sandwich thin-walled microbeams are greatly influenced by the variations of parameters mentioned earlier. The microbeams with the size effect are predicted to be much stiffer than their macro counterparts. Some benchmark results can be used as a reference for future studies. [ABSTRACT FROM AUTHOR]

This paper presents flexural analysis of composite and sandwich beams using a quasi-3D theory, which considers simultaneously three effects such as normal and shear deformation as well as anisotropy coupling. The axial and transverse displacements are assumed to be cubic and parabolic variation through the beam depth. In order to solve problem, two-node C 1 beam elements with six degrees of freedom per node are developed. Numerical examples are carried out and the results are compared with those available in literature to validate the accuracy of the present theory. The effects of fibre angle, lay-up and span-to-height ratio on displacements and stresses are studied. Some new results, which can be useful for future references, are also given. [ABSTRACT FROM AUTHOR]

Although machine learning models have been employed for the compressive strength (CS) of cement-based mortar containing metakaolin, it is difficult to understand how they work due to "black-box" nature. In order to explain the involved mechanism, Categorical Gradient Boosting (CatBoost) model with feature importance, feature interaction, partial dependence plot (PDP) and SHapley Additive exPlanations (SHAP) is proposed in this paper. A dataset consisting of 424 samples with six input variables is used to build the CatBoost model, which has optimal performance by tuning a set of seven hyper-parameters using sequential model-based optimization. Five quantitative measures (R 2 , MAE, RMSE, a10-, a20-index) are employed to evaluate the accuracy and the obtained results are superior to the previous study. It is from feature importance that the most significant input variable involving the CS is water-to-binder ratio, followed by age of specimen and cement grade. The strongest feature interaction is between water-to-binder ratio and metakaolin. A comprehensive parametric study is carried out via SHAP and PDP to investigate the effects of all input variables on the CS of cement-based mortar. • CatBoost model is used to predict compressive strength of mortar containing metakaolin. • Feature interaction, partial dependence plot and SHapley Additive exPlanations are illustrated. • The comparison with previous study shows higher prediction accuracy. • The strongest feature interaction is between water-to-binder ratio and metakaolin. [ABSTRACT FROM AUTHOR]