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Mechanics Based Design of Structures and Machines (15397742)53(6)pp. 4104-4131
In present study, a numerical analysis of a sandwich structure with a lattice core consisting of two outer layers of sheets and an internal lattice core was undertaken. A two-step finite element method was applied to explore their mechanical behavior. The investigation primarily focused on evaluating the natural frequencies, critical buckling load, and maximum deformations of these plates. In first step, the finite element method was used to meticulously calculate the extensional stiffness, bending-extensional coupling stiffness, and bending stiffness matrices for a unit cell of lattice core. A cell was modeled in SAP2000 initially and then the entire structure was expanded. After that, in second step, the response of lattice structures was conveniently calculated by employing the stiffness matrices that were calculated in the first step. The obtained results were thoroughly compared with existing literature, ensuring the precision and reliability of the findings. These findings offer valuable insights for the design and optimization of sandwich structures with lattice core configurations across various engineering applications. © 2024 Taylor & Francis Group, LLC.
Structural Engineering and Mechanics (12254568)89(2)pp. 181-197
A numerical method is presented in this paper, for buckling analysis of thin arbitrary stiffened composite cylindrical shells under axial compression. The stiffeners can be placed inside and outside of the shell. The shell and stiffeners are operated as discrete elements, and their interactions are taking place through the compatibility conditions along their intersecting lines. The governing equations of motion are obtained based on Koiter's theory and solved by utilizing the principle of the minimum potential energy. Then, the buckling load coefficient and the critical buckling load are computed by solving characteristic equations. In this formulation, the elastic and geometric stiffness matrices of a single curved strip of the shell and stiffeners can be located anywhere within the shell element and in any direction are provided. Moreover, five stiffened composite shell specimens are made and tested under axial compression loading. The reliability of the presented method is validated by comparing its numerical results with those of commercial software, experiments, and other published numerical results. In addition, by using the ANSYS code, a 3-D finite element model that takes the exact geometric arrangement and the properties of the stiffeners and the shell into consideration is built. Finally, the effects of Poisson's ratio, shell length-to-radius ratio, shell thickness, cross-sectional area, angle, eccentricity, torsional stiffness, numbers and geometric configuration of stiffeners on the buckling of stiffened composite shells with various end conditions are computed. The results gained can be used as a meaningful benchmark for researchers to validate their analytical and numerical methods. Copyright © 2024 Techno-Press, Ltd.
Acta Mechanica (16196937)235(12)pp. 7059-7082
This paper develops a size-dependent Kirchhoff plate model for bending and free vibration analyses using a semi-analytical higher-order finite strip method (H-FSM) based on the nonlocal strain gradient theory (NSGT). To satisfy the various longitudinal boundary conditions, the continuous trigonometric function series and the interpolation polynomial functions are employed in the transverse direction. In solving nanoplate problems using the H-FSM, the higher-order polynomial shape functions (higher-order Hermitian shape functions) are utilized to evaluate the second derivatives, in addition to the displacement and first derivative. The stiffness and mass matrices, and force vector of the nanoplates are derived using the weighted residual method. A numerical study is conducted to investigate the impact of different factors, such as boundary conditions, nonlocal and strain gradient parameters, aspect ratio, and types of transverse loading. The Navier solution is utilized to analyze the effects of material length scale parameters on bending and free vibration responses of nanoplates for preliminary comparisons. The numerical results show that, when the transverse load on the nanoplate is uniform or hydrostatic and the plate has a CCCC boundary condition, the nonlocal effect does not affect the deflection results and is the same as the obtained results in the local mode. © The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2024.
Archives of Civil and Mechanical Engineering (16449665)24(2)
In this paper, a new model for porous structures in functionally graded plates (FGPs) is introduced that under significant differences in constitutive material properties and high porosity ratios, the difference in elasticity modulus of the suggested pattern reaches twice as many as the previous model. This study is based on the finite strip method, incorporating Eringen nonlocal elasticity and third-order shear deformation theory, to create standard and geometric stiffness matrices for mechanical and thermal buckling analyses of functionally graded porous nanoplates (FGPNPs). The procedure is founded on Lagrangian and Hermitian shape functions to account for significant shear deformation effects in thick plates, and all in-plane displacements are applied in the geometric matrix based on the virtual work principle. Various factors like boundary conditions, porosity distributions, temperature variations, and nonlocal parameter are investigated for their impact on the mechanical and thermal buckling loads of FGPNPs. The findings reveal the substantial influence of size effects on thick porous nanoplate evaluations. Mechanical analysis shows that O-, V-, X-shaped and uniform patterns exhibit the best performance against mechanical loads, respectively. Despite the material properties deteriorating with increased porosity ratios, thermal resistance is improved. The new uniform pattern performs the best under uniform loading, and V-shaped porous structures excel at strength against nonlinear loading. However, the X-shaped model exhibits the lowest thermal resistance in both conditions. © Wroclaw University of Science and Technology 2024.
Mechanics of Advanced Materials and Structures (15210596)31(9)pp. 2008-2028
The buckling behavior of moderately thick and thick stiffened composite plates with different stiffener layouts is formulated based on the higher-order shear deformation theory. This investigation is performed under axial compression using the Finite Strip Method and experiment. The effects of dimensions, orientation, eccentricity, torsional stiffness, position and geometric configuration of stiffeners on the buckling load coefficient are achieved by employing the principle of minimum potential energy. Six grid-stiffened composite plate specimens with ortho-grid, angle-grid, and orthotropic-grid stiffeners are tested. The results of the presented method show good outcomes with those of experimental tests and the finite element ANSYS code. © 2022 Taylor & Francis Group, LLC.
Mechanics Based Design of Structures and Machines (15397742)51(4)pp. 2251-2278
The Finite Strip Method (FSM) was employed to study the buckling behavior of laminated glass fiber-reinforced polymer (GFRP) stiffened plates with different boundary conditions under axial compression. The theoretical formulation was established based on the first-order shear deformation theory (FSDT) for the thin plate and the stiffener. In this formulation, the stiffeners are not required to be placed on the nodal lines. This feature is considered useful in modeling the stiffened plates in which the stiffener elements are placed arbitrarily in complex planforms. Experimental, numerical and analytical studies were conducted to investigate the effects of the plate width-to-thickness ratio, the stiffener thickness-to-width ratio, dimensions, angle, eccentricity, torsional stiffness and geometric configuration of stiffeners on axial buckling capacity. Furthermore, the obtained results of the analytical method were compared with experimental results and ANSYS code to show its accuracy and convergence. The advantages of the present are that number of elements is much less and the mesh refinement process is much more convenient than commercial finite element software and traditional finite element method (FEM). Therefore, time consumed for analysis is less than the codes which work based on the finite element method. © 2021 Taylor & Francis Group, LLC.
Journal of Anatomy (14697580)240(2)pp. 305-322
Statistical data pertaining to anatomic variations of the human talus contain valuable information for advances in biological anthropology, diagnosis of the talar pathologies, and designing talar prostheses. A statistical shape model (SSM) can be a powerful data analysis tool for the anatomic variations of the talus. The main concern in constructing an SSM for the talus is establishing the true geometric correspondence between the talar geometries. The true correspondence complies with biological and/or mathematical homologies on the talar surfaces. In this study, we proposed a semi-automatic approach to establish a dense correspondence between talar surfaces discretized by triangular meshes. Through our approach, homologous salient surface features in the form of crest lines were detected on 49 talar surfaces. Then, the point-wise correspondence information of the crest lines was recruited to create posterior Gaussian process morphable models that non-rigidly registered the talar meshes and consequently established inter-mesh dense correspondence. The resultant correspondence perceptually represented the true correspondence as per our visual assessments. Having established the correspondence, we computed the mean shape using full generalized Procrustes analysis and constructed an SSM by means of principal component analysis. Anatomical variations and the mean shape of the talus were predicted by the SSM. As a clinically related application, we considered the mean shape and investigated the feasibility of designing universal talar prostheses. Our results suggest that the mean shape of (the shapes of) tali can be used as a scalable shape template for designing universal talar prostheses. © 2021 Anatomical Society
European Journal of Mechanics, A/Solids (09977538)95
In this paper, a semi-analytical higher-order finite strip method is developed based on the nonlocal strain gradient theory (NSGT) for buckling analysis of orthotropic nanoplates. NSGT contains two material length scale parameters related to the nonlocal and strain gradient effects. To consider the effect of the strain gradient in the governing equation of the plate in the transverse direction, the higher-order polynomial shape functions (higher-order Hermitian shape functions) are utilized to assess the second derivatives, in addition to the displacement and first derivatives. Also, some numerical study is presented on the effects of different factors such as boundary conditions, nonlocal and strain gradient parameters, aspect ratio, and different types of in-plane loading for the isotropic and orthotropic rectangular nanoplate to verify the proposed formulation. In the following, a relation for the nanoplates based on the nonlocal strain gradient theory using the Navier method is extracted and presented for preliminary comparisons. According to the proposed relation, it is shown that in simply supported nanoplates, if the non-local parameter is equal to the second power of the strain gradient parameter, the responses obtained for the nanoplates are equal to the locally available responses. © 2022 Elsevier Masson SAS
Thin-Walled Structures (02638231)172
In this paper dynamic buckling of different kinds of sandwich plates under harmonic axial load is analyzed by using combination of numerical finite strip analysis and Bolotin's solution which offer a kind of method to find the regions of dynamic instability for dynamic stability of plates. The sandwich plates which are considered here consist of homogeneous core sandwich plates, functionally graded sandwich plates, trapezoidal corrugated core sandwich plates, Z and C form corrugated core sandwich plates and truss core sandwich plates. Third order shear deformation theory is used as numerical method to study stability regions of sandwich plates. The effect of damping is neglected and the effect of length to thickness ratio, different boundary conditions, number of face sheet layers and different geometry and material properties of core is studied. According to the results the dynamic buckling should also be investigated in sandwich plate. Also, according to the results, it is observed that the finite strip method has an acceptable accuracy in investigating the dynamic buckling of sandwich plates. © 2021 Elsevier Ltd
Structures (23520124)39pp. 739-764
In present paper, the behavior of tapered composite plate under low-velocity impact was studied. The tapered plates were used in many structures according to their stiffness to weight ratio, while, the behavior of such plates did not evaluate under impact load in the literatures. Geometrically nonlinear Von-Karman strain was taken into account with respect to large deformations. The spline finite strip method (SFSM) was used to predict the impact behavior of composite laminates. The numerical fourth-order Runge-Kutta integration technique was used to solve the governing differential equations. The displacement field was defined according to the refined plate theory. The four most common internal taper configurations were considered. Local indentation was modeled with the help of contact Hertz's laws. The governing differential equation was written based on the principal of virtual displacement and Hamilton's principle for dynamic systems. The obtained results on eccentric impact showed that contact force and indentation are increased when indenter contact near supports. © 2022 Institution of Structural Engineers
Structures (23520124)33pp. 4514-4537
This research presents a study on the buckling behaviour of the stiffened cylindrical shells made of laminated glass fibre-reinforced polymer (GFRP) with arbitrary stiffeners under axial compression by using the curved finite strip method. The stiffeners can be positioned at the inner and outer surfaces of the shell, and is no need to be located on the nodal lines. The governing equations of motion are extracted from Koiter's theory based on the first-order shear deformation theory and solved employing the principle of the minimum potential energy. Then, both the critical buckling load and the buckling load coefficient are calculated by solving characteristic equations. Boundary conditions considered are simple-simple, clamped–clamped, and clamped-simple supports. A relatively high-order polynomial function for the displacement components in the transverse direction is assumed for the shell and the stiffeners. A displacement model is assumed with twenty-four degrees of freedom arranged at four nodal lines for each strip. To validating the proposed method, the results of this investigation are compared with the finite element, experimental and other published numerical results. The benefits of this method are that number of elements, and therefore time consumed for analysis is much less, and the mesh refinement process is much more convenient than the conventional finite element method. Finally, the effects of the different parameters such as Poisson's ratio, boundary condition, thickness variations and geometrical parameters of shell and stiffeners, angle, eccentricity, torsional stiffness, cross-sectional area, number of stiffeners on the buckling are studied. The results obtained can be employed as a significant benchmark for researchers to verify their analytical and numerical approaches. © 2021 Institution of Structural Engineers
Structural Engineering and Mechanics (12254568)75(2)pp. 247-269
A finite strip formulation was developed for buckling and free vibration analysis of laminated composite plates based on different shear deformation plate theories. The different shear deformation theories such as Zigzag higher order, Refined Plate Theory (RPT) and other higher order plate theories by variation of transverse shear strains through plate thickness in the parabolic form, sine and exponential were adopted here. The two loaded opposite edges of the plate were assumed to be simply supported and remaining edges were assumed to have arbitrary boundary conditions. The polynomial shape functions are applied to assess the in-plane and out-of-plane deflection and rotation of the normal cross-section of plates in the transverse direction. The finite strip procedure based on the virtual work principle was applied to derive the stiffness, geometric and mass matrices. Numerical results were obtained based on various shear deformation plate theories to verify the proposed formulation. The effects of length to thickness ratios, modulus ratios, boundary conditions, the number of layers and fiber orientation of cross-ply and angle-ply laminates were determined. The additional results on the same effects in the interaction of biaxial in-plane loadings on the critical buckling load were determined as well. Copyright © 2020 Techno-Press, Ltd.
A semi analytical finite strip method was developed in present article for buckling of laminated composite plates with piezoelectric layers based on different plate theories. Displacement functions of plate were evaluated using a continuous harmonic function series in the longitudinal direction that satisfies the simply support boundary condition and a piecewise interpolation polynomial in the transverse direction. The analysis conducted based on Reddy's third order shear deformation theory, first order shear deformation theory and classical laminated plate theory. So, considering the strain-displacement relations and stress-strain relations, the standard stiffness and geometry matrices were evaluated using the virtual work principle. The numerical results of buckling of piezoelectric laminated plates based on different plate theories were presented. The effects of different electric conditions, length to thickness ratio and fiber orientation were investigated through the numerical examples. © CCM 2020 - 18th European Conference on Composite Materials. All rights reserved.
European Journal of Mechanics, A/Solids (09977538)74pp. 242-256
A finite strip method was developed for buckling and free vibration analysis of piezoelectric laminated composite plates based on various plate theories such as Zigzag, Refined plate and other higher order shear deformation theory by variation of transverse shear strains through plate thickness in the form of parabolic, sine and exponential. The plate edge conditions are considered to be simply supported and the polynomial shape functions are used to evaluate the in–plane and out–of–plane deflection and rotation of the normal cross section of plates in transverse direction. Numerical results were obtained based on various shear deformation plate theories to verify the proposed method. The effects of length to thickness ratio and fiber orientation of cross–ply and angle–ply laminate were presented. Also, the effect of different electrical conditions on the critical buckling load under in–plane forces and strains is investigated and electrical buckling load and natural frequency of piezoelectric laminate composite plates are calculated through numerical examples. In addition, the new results on the effect of piezoelectric layers thickness, placement of piezoelectric layers and also the effect of length to thickness ratio in the interaction of biaxial in–plane loading on critical buckling load were studied. © 2018 Elsevier Masson SAS
Journal of Thermal Stresses (01495739)41(2)pp. 182-203
A complex finite strip method was used to study the buckling of functionally graded plates (FGPs) under thermal and mechanical (longitudinal, transverse, and shear in-plane) loading. The mechanical characteristics of FGPs were assumed to vary through the thickness, according to power law distribution. The nonlinear temperature distribution in the direction of the plate thickness was assumed according to thermal conduction steady state conditions. In complex finite strip method, the polynomial Hermitian functions were assumed in the transverse direction and the complex exponential functions were used in the longitudinal direction to evaluate the standard and geometric stiffness matrices that have the ability of calculating the critical shear stress in contrast to trigonometric shape functions. The solution was obtained by the minimization of the total potential energy and solving the corresponding eigenvalue problem. In addition, numerical results for FGPs with different boundary conditions were presented and compared with those available in the literature and the interaction curves of mechanical and thermal buckling capacity of FGPs were obtained. © 2018 Taylor & Francis.
Thin-Walled Structures (02638231)131pp. 88-101
The effect of hygrothermal conditions such as temperature and moisture on free vibration frequency and buckling load of composite laminated plates was investigated in present article. For this purpose, the effect of changing in material characteristics with changing in temperature and moisture on buckling capacity and natural frequency of plates with different end conditions and biaxial loading was evaluated. In addition, the effect of delamination of layers on buckling load and natural frequency of plate was studied in different situations. The finite strip method was used in present paper to calculate the critical load of plate considering first-order shear deformation theory. In finite strip formulation for evaluating the displacement field of each strip, the trigonometric shape functions were used in longitudinal direction and the Hermitian and linear shape functions were used for out–of–plane and in–plane transverse direction, respectively. The place and dimension of delaminating layers was modelled by separating the adjacent elements and reconstructing the standard, geometric, force and mass matrices, so, the critical load and natural frequency of laminated plates was calculated in different configurations. © 2018 Elsevier Ltd
European Journal of Mechanics, A/Solids (09977538)68pp. 38-52
Time depended deformation and critical buckling load of viscoelastic thick plates were studied using finite strip method with the trigonometric functions in longitudinal direction and the polynomial functions in transverse direction. The plates were considered to be thick and the third order shear deformation theory was used to consider the effect of shear stresses in thickness. The mechanical properties of the material were considered to be linear viscoelastic by expressing the relaxation modulus in terms of Prony series. Time history of maximum deflection of viscoelastic plates subjected to transverse loading and unloading on plates was calculated using a fully discretized formulation. In addition, the critical in–plane load of plates was calculated by a nonlinear procedure in different times of loading. Moreover, the effect of thickness and the interaction of biaxial in–plane loading on critical load of plate were studied. © 2017 Elsevier Masson SAS
European Journal of Mechanics, A/Solids (09977538)61pp. 1-13
In the present article the mechanical instability and free vibration of FGM micro-plate based on the modified strain gradient theory were studied using the spline finite strip method. By daily increase in the application of micro-scale structures, developing theories were become essential to account in a way for the size-reduction effect. The modified strain gradient theory based on three length scale parameters, has the capability of evaluating structures at the micro size level. Considering the obtained results, it was clear that increasing the length-scale parameter would increase the critical buckling load and the vibration frequency, similar to the macroscopic case. In addition, increasing the power of volume fraction module decreases the critical load and the natural frequency of micro plate. Finally, the effect of length-scale parameter, boundary conditions, volume fraction module and dimensions of the micro-plate on critical loading and natural frequency of micro-plate were studied. © 2016 Elsevier Masson SAS
International Journal of Structural Stability and Dynamics (02194554)16(9)
The Hp-Cloud meshless method was developed to study the dynamic analysis of arbitrarily shaped thin plates with intermediate point supports. By proposing a special pattern for the influence radius of nodes and a polynomial type of enrichment function, the Hp-Cloud shape functions with Kronecker delta property were constructed. They can satisfy the zero deflection conditions for the field nodes at the point supports. The results obtained from these shape functions agree well with the previous ones, showing good accuracy and convergence. For plates with sharp corners, it is not possible to construct the Hp-Cloud shape function with Kronecker delta property. To this end, the Lagrange multiplier method was used for enforcing the boundary conditions. The computations were carried out by the Ritz method, and the cell structure method is refined to improve the speed and accuracy of numerical integration on the subscription surface of clouds intersecting with the plate boundaries. Using the algorithm developed, the natural frequencies of plates of various shapes and support patterns were computed. By increasing the number of point supports on the plate edges, the natural frequencies computed of the plate tend to those of the simply supported plate. Appropriate pattern of point supports distribution was presented for modeling the simply supported plates of various shapes by comparing the corresponding natural frequencies. © 2016 World Scientific Publishing Company.
Mechanics of Advanced Materials and Structures (15210596)22(8)pp. 655-669
A semi-analytical fully discretized finite strip method is developed to investigate the pre-buckling and local buckling of viscoelastic plates with different boundary conditions subjected to time-dependent loading. The mechanical properties of the material are considered to be linear viscoelastic by expressing the relaxation modulus in terms of Prony series. The fully discretized finite strip equations are developed using a two-point recurrence formulation, which leads to a computationally superior formulation. Time history of maximum deflection of plates with different end conditions is calculated. The effects of thickness, length of plate, and transverse loading on critical buckling load are also studied. Copyright © 2015 Taylor & Francis Group, LLC.
Aerospace Science and Technology (12709638)47pp. 356-366
The buckling of a thin FGM microplate subjected to mechanical and thermal loading is evaluated using the spline finite strip method, based on modified couple stress theory. Regarding thickness, the features of the FGM plate are assumed as being variable according to the law's proposed model. The spline finite strip method are used for calculating the buckling load and critical temperature by solving an eigenvalue problem. The results showed that reduction in size did not affect interaction of forces. Also, the length scale parameter, volume fraction modulus, different boundary conditions and the dimensions of the plate are considered. © 2015 Elsevier Masson SAS. All rights reserved.
Composites Part B: Engineering (13598368)56pp. 222-231
A linear finite strip plate element based on the first order shear deformation theory is considered for the analysis of viscoelastic plates. The plate end conditions are considered to be simply supported and the polynomial shape functions are used to evaluate the deflection of plates in transverse direction. The mechanical properties of the material are considered to be linear viscoelastic by expressing the relaxation modulus in terms of Prony series. The time history of maximum deflection of viscoelastic plates subjected to loading and unloading is calculated. In addition, a nonlinear procedure is used to calculate the changing of in-plane critical load of plate with time. Moreover, the effect of thickness and the interaction of biaxial loading on critical load of plate are studied. © 2013 Elsevier Ltd. All rights reserved.
Composite Structures (02638223)100pp. 205-217
A semi analytical finite strip method is developed for the analysis of viscoelastic plates with different end conditions using bubble functions. Each plate may be subjected to different types of out-of-plane and in-plane loading. The displacement functions of plate are evaluated using a continuous harmonic function series that satisfies the boundary conditions in the longitudinal direction and a piecewise interpolation polynomial in the transverse direction. The mechanical properties of the material are considered to be linear viscoelastic by expressing the relaxation modules in terms of Prony series. The fully discretized finite strip equations are developed using a two point recurrence formulation. Time history of maximum deflection of plates with different end conditions is calculated in the present study. In addition, the effect of unloading on plates is evaluated. Moreover, a nonlinear approach is used to calculate the critical load of plates subjected to in-plane compressive loads. © 2013 Elsevier Ltd.
Composite Structures (02638223)90(1)pp. 92-99
A finite strip method is presented to predict local, distortional, and lateral buckling of composite fiber reinforced plastic (FRP) structural plates. Each plate may be subjected to a combination of longitudinal compression, longitudinal in-plane bending, or shear stress. A sinusoidal function is assumed in the longitudinal direction for a buckling mode of whatever type and a polynomial function is used in the transversal direction. The critical stress and critical moment of I-shape and box and channel sections under bending and uniform loading are obtained by solving an eigenvalue problem. Using this solution technique, a simple expression is developed for prediction of I-shape section beams' buckling stresses in three design curves. The critical stresses for different Ex / Ey values are calculated using the design curves. © 2009 Elsevier Ltd. All rights reserved.
