Shapour Moradi - Academia.edu (original) (raw)
Papers by Shapour Moradi
Computers & Structures, Mar 1, 1999
The delamination buckling response of a composite panel containing through-the-width delamination... more The delamination buckling response of a composite panel containing through-the-width delamination is numerically modeled using a solution that is based on the differential quadrature method (DQM). The composite is modeled as a general one-dimensional beam–plate having a through-the -width delamination that can be at any arbitrary location through its thickness; hence, dividing the domain into four regions. The DQM is
International journal of engineering. Transactions A: basics, Apr 1, 2020
The rotating machinery is a common class of machinery in the industry. The root cause of faults i... more The rotating machinery is a common class of machinery in the industry. The root cause of faults in the rotating machinery is often faulty rolling element bearings. This paper presents a novel technique using artificial neural network learning for automated diagnosis of localized faults in rolling element bearings. The inputs of this technique are a number of features (harmmean and median), which are extracted from the vibration signals of the test data. Effectiveness and novelty of this proposed method are illustrated by using the experimentally obtained the bearing vibration data based on laboratory application. In this research, based on the fast kurtogram method in the time-frequency domain, a technique for the first time is presented using other types of statistical features instead of the kurtosis. For this study, the problem of four classes for bearing fault detection is studied using various statistical features. This study is conducted in four stages. At first, the stability of each feature for each fault mode is investigated, then resistance to load change as well as failure growth is studied. At the end, the resolution and fault detection for each feature using the comparison with a determined pattern and the coherence rate is calculated. From the above results, the best feature that is both resistant and repeatable to different variations, as well as the suitable accuracy of detection and resolution, is selected and with comparing to the kurtosis feature, it is found that this feature is not in a good condition in compared with other statistical features such as harmmean and median. The results show that the accuracy of the proposed approach is 100% by using the proposed neural network, even though it uses only two features.
Journal of Mechanical Science and Technology, 2013
This study presents an inverse procedure to identify multiple cracks in beams using an evolutiona... more This study presents an inverse procedure to identify multiple cracks in beams using an evolutionary algorithm. By considering the crack detection procedure as an optimization problem, an objective function can be constructed based on the change of the eigenfrequencies and some strain energy parameters. Each crack is modeled by a rotational spring. The changes in natural frequencies due to the presence of the cracks are related to a damage index vector. Then, the bees algorithm, a swarm-based evolutionary optimization technique, is used to optimize the objective function and find the damage index vector, whose positive components show the number and position of the cracks. A second objective function is also optimized to find the crack depths. Several experimental studies on cracked cantilever beams are conducted to ensure the integrity of the proposed method. The results show that the number of cracks as well as their sizes and locations can be predicted well through this method.
Journal of Adhesion, Apr 20, 2022
Applied and Computational Mechanics, Jun 1, 2021
This paper aims to discuss the vibration analysis of the post-buckled cracked axially functionall... more This paper aims to discuss the vibration analysis of the post-buckled cracked axially functionally graded (AFG) beam. The nonlinear equations of motion of the Euler-Bernoulli beam are derived using the equilibrium principles. Then, these differential equations are converted into a set of algebraic ones using the differential quadrature (DQ) method and solved by an arc-length strategy. The resulted displacement field from the post-buckling analysis is assumed to be the equilibrium state of vibration analysis, and an eigenvalue problem is derived. By solving this linear eigenvalue problem, both the natural frequencies and mode shapes of the beam are calculated. The validation of results in comparison with a similar work shows a good agreement. The effect of several parameters such as the extensible and inextensible clamped-clamped boundary conditions, initial geometric imperfection, crack's depth, and crack's location on the natural frequencies and mode shapes are investigated in detail.
Structural Engineering and Mechanics, 2018
Structural Health Monitoring-an International Journal, Jan 3, 2017
Crack identification in engineering structures has been widely investigated by researchers. Most ... more Crack identification in engineering structures has been widely investigated by researchers. Most of the literature on multiple crack identification, however, has focused on rather simple structures like beams and it is often assumed that the number of cracks is known while this is not a practical assumption. In this article, multiple crack identification in frame structures is investigated based on experimental vibration data using the Bayesian model class selection and swarm-based optimization methods to identify both the number of cracks and their characteristics. To this end, first, the numerical model of the intact frame is updated based on the natural frequencies of the intact state using the particle swarm inspired multi-elitist artificial bee colony algorithm. After updating the intact model of the structure, a set of numerical models of the cracked frame with different numbers of cracks is constructed. Since the number of cracks is not known a priori, the Bayesian model class selection is employed to find the most plausible model class in order to predict the number of cracks. Then, the parameters of the cracks are identified using the particle swarm inspired multi-elitist artificial bee colony algorithm. Instead of pinpointing to one optimal solution obtained after a large number of function evaluations, a set of best solutions whose objective values are less than 10 25 are recorded and the regions where the best solutions are concentrated are identified to see how the solution would differ if less number of function evaluations is employed. To fully assess the effectiveness of this approach, both numerical and experimental examples are utilized. The results confirm the effectiveness of the proposed method for identifying multiple cracks in the frames using a few experimental natural frequencies of the structure. The effect of using more natural frequencies on the accuracy of the location and depth of the cracks is also studied.
Structural and Multidisciplinary Optimization, Feb 27, 2010
... Finite element model updating using bees algorithm Shapour Moradi · Laleh Fatahi · Pejman Raz... more ... Finite element model updating using bees algorithm Shapour Moradi · Laleh Fatahi · Pejman Razi ... Gradient-based tech-S. Moradi (B) · L. Fatahi · P. Razi Mechanical Engineering Department, Shahid Chamran University, Ahvaz, 61355, Iran e-mail: moradis@scu.ac.ir ...
AIAA Journal, 1998
The differential quadrature method (DQM) is used to analyze the one-dimensional buckling of a lam... more The differential quadrature method (DQM) is used to analyze the one-dimensional buckling of a laminated composite beam plate having an across-the-width delamination located at an arbitrary depth and an arbitrary location along its span. A beam theory with shear deformation is used in formulating the problem. Several case studies are conducted to examine the buckling response of laminates hosting such a delamination. Using DQM, the system of equilibrium equations and the boundary conditions are transformed into a system of linear algebraic eigenvalue equations that are solved by a standard eigensolver. The influences of several parameters that affect the buckling strength of such laminates are investigated. The investigated parameters are the shear deformation factor, the length of the delamination, and the through-the-thickness and longitudinal positions of the delamination. The results verify the accuracy and efficiency of DQM.
<jats:title>Abstract</jats:title> <jats:p>In this paper a package is introduced... more <jats:title>Abstract</jats:title> <jats:p>In this paper a package is introduced which handles shape optimization in 2-dimensional elasticity problems where Boundary Element Method is used for the analysis phase affording a large reduction in the problem dimensionality together with a variant of the Method of Center Points for the optimization phase. This optimization method allows a high reduction in the number of constraints considered in each step, as well as low number of cycles, resulting in notable overall efficiency.</jats:p> <jats:p>Design variables in optimum shape determination consists of basic nodal coordinates for B-spline functions as the means to define smooth boundary curves. Maximum stress and/or displacements at critical boundary points are observed as constraints in each cycle of the procedure.</jats:p> <jats:p>Three classical case examples are solved successfully, and the results are compared with those of others, illustrating the superior capabilities of the program package.</jats:p>
WIT transactions on engineering sciences, 1970
In this study the differential quadrature method (DQM) is used to model the postbuckling analysis... more In this study the differential quadrature method (DQM) is used to model the postbuckling analysis of imperfect laminated composite beams having multiple delaminations and subject to axial compressive load. The delaminations are considered to be through-the-width in an arbitrary locations, through-thethickness and along the span of the beam. A nonlinear beam theory is used to formulate the problem. To model the delaminated beam, the beam is divided into a series of regions bounded by the delaminated segments. Using DQM, the system of equilibrium equations and the boundary conditions are transformed into a system of nonlinear algebraic equations that are solved by an arc-length strategy. The contact effect between the delaminated surfaces and the delamination growth due to the opening of the delaminated sections under the compressive load were not considered in this study. To validate the integrity of the DQM, the numerical results obtained from a series of case studies are compared with those of the other published results. These comparisons would confirm the efficiency and accuracy of the DQM.
Mechanical Systems and Signal Processing, Jun 1, 2022
Applied Mechanics and Materials, Nov 1, 2012
This article focuses on the application of the Fourier-expansion based differential quadrature me... more This article focuses on the application of the Fourier-expansion based differential quadrature method (FDQM) for the buckling analysis of ring-stiffened composite laminated cylindrical shells. Displacements and rotations are expressed in terms of Fourier series expansions in longitudinal direction and their first order derivatives are approximated with FDQM in circumferential direction. The &amp;amp;#39;smeared stiffener&amp;amp;#39; approach is adopted for the stiffeners modeling. Two FORTRAN programs prepared for linear and nonlinear analysis and results were compared by ABAQUS finite element software. Buckling loads of stiffened and unstiffened shells considering the effects of changes in shell and stiffener geometric and material properties and also shell lay-ups are investigated.
Applied and Computational Mechanics, Dec 1, 2017
In this study, a hybrid method is proposed to investigate the nonlinear vibrations of pre-and pos... more In this study, a hybrid method is proposed to investigate the nonlinear vibrations of pre-and post-buckled rectangular plates for the first time. This is an answer to an existing need to develop a fast and precise numerical model which can handle the nonlinear vibrations of buckled plates under different boundary conditions and plate shapes. The method uses the differential quadrature element, arc-length, harmonic balance and direct iterative methods. The governing differential equations of plate vibration have been extracted considering shear deformations and the initial geometric imperfection. The solution is assumed to be the sum of the static and dynamic parts which upon inserting them into the governing equations, convert them into two sets of nonlinear differential equations for static and dynamic behaviors of the plate. First, the static solution is calculated using a combination of the differential quadrature element method and an arc-length strategy. Then, putting the first step solutions into the dynamic nonlinear differential equations, the nonlinear frequencies and modal shapes of the plate are extracted using the harmonic balance and direct iterative methods. Comparing the obtained solutions with those published in the literature confirms the accuracy and the precision of the proposed method. The results show that an increase in the nonlinear vibration amplitude increases the nonlinear frequencies.
Applied Mathematical Modelling, Jul 1, 2014
Vibration analysis of cracked post-buckled beam is investigated in this study. Crack, assumed to ... more Vibration analysis of cracked post-buckled beam is investigated in this study. Crack, assumed to be open, is modeled by a massless rotational spring. The beam is divided into two segments and the governing nonlinear equations of motion for the post-buckled state are derived. The solution consists of static and dynamic parts, both leading to nonlinear differential equations. The differential quadrature has been used to solve the problem. First, it is applied to the equilibrium equations, leading to a nonlinear algebraic system of equations that will be solved utilizing an arc length strategy. Next, the differential quadrature is applied to the linearized dynamic differential equations of motion and their corresponding boundary and continuity conditions. Upon solution of the resulting eigenvalue problem, the natural frequencies and mode shapes of the cracked beam are extracted. Several experimental as well as numerical case studies are performed to demonstrate the effectiveness of the proposed method. The investigation also includes an examination of several parameters influencing the dynamic behavior of the problem. The results show that the position and size of the crack as well as the geometric imperfection and applied load largely affect the modal shapes and natural frequencies of the beam.
Journal of Pressure Vessel Technology-transactions of The Asme, Aug 30, 2017
Linearized buckling analysis of functionally graded shells of revolution subjected to displacemen... more Linearized buckling analysis of functionally graded shells of revolution subjected to displacement-dependent pressure, which remains normal to the shell's middle surface throughout the deformation process, is described in this work. Material properties are assumed to be varied continuously in the thickness direction according to a simple power law distribution in terms of the volume fraction of a ceramic and a metal. The governing equations are derived based on the first-order shear deformation theory, which accounts for through the thickness shear flexibility with Sanders type of kinematic nonlinearity. Displacements and rotations in the shell's middle surface are approximated by combining polynomial functions in the meridian direction and truncated Fourier series with an appropriate number of harmonic terms in the circumferential direction. The load stiffness matrix, also known as the pressure stiffness matrix, which accounts for the variation of load direction, is derived for each strip and after assembling resulted in the global load stiffness matrix of the shell, which may be unsymmetric. The load stiffness matrix can be divided into two unsymmetric parts (i.e., load nonuniformity and unconstrained boundary effects) and a symmetric part. The main part of this research is to quantify the effects of these unsymmetries on the follower action of lateral pressure. A detailed numerical study is carried out to assess the influence of various parameters such as power law index of functionally graded material (FGM) and shell geometry interaction with load distribution, and shell boundary conditions on the follower buckling pressure reduction factor. The results indicate that, when applied individually, unconstrained boundary effect and longitudinal nonuniformity of lateral pressure have little effect on the follower buckling reduction factor, but when combined with each other and with circumferentially loading nonuniformity, intensify this effect.
Computational Mechanics, Sep 21, 2000
The application of a robust numerical method, namely the differential quadrature method (DQM) for... more The application of a robust numerical method, namely the differential quadrature method (DQM) for the analysis of buckling and postbuckling of laminated composite plates is introduced. The method is combined with an arc-length strategy to solve the resulting system of nonlinear equations. The treatment accounts for the effect of large deformation by including the von Karman strains. Imperfections in the
Steel and Composite Structures, Jan 20, 2017
International Journal of Pressure Vessels and Piping, Nov 1, 2013
The problem of crack detection in cylindrical shell structures is investigated.> To do this, the ... more The problem of crack detection in cylindrical shell structures is investigated.> To do this, the differential quadrature method and bees algorithm has been used.> Numerical and experimental studies on the cracked free-free shells were conducted.> The results showed that the crack locations, sizes and depths were predicted well.>
Computers & Structures, Mar 1, 1999
The delamination buckling response of a composite panel containing through-the-width delamination... more The delamination buckling response of a composite panel containing through-the-width delamination is numerically modeled using a solution that is based on the differential quadrature method (DQM). The composite is modeled as a general one-dimensional beam–plate having a through-the -width delamination that can be at any arbitrary location through its thickness; hence, dividing the domain into four regions. The DQM is
International journal of engineering. Transactions A: basics, Apr 1, 2020
The rotating machinery is a common class of machinery in the industry. The root cause of faults i... more The rotating machinery is a common class of machinery in the industry. The root cause of faults in the rotating machinery is often faulty rolling element bearings. This paper presents a novel technique using artificial neural network learning for automated diagnosis of localized faults in rolling element bearings. The inputs of this technique are a number of features (harmmean and median), which are extracted from the vibration signals of the test data. Effectiveness and novelty of this proposed method are illustrated by using the experimentally obtained the bearing vibration data based on laboratory application. In this research, based on the fast kurtogram method in the time-frequency domain, a technique for the first time is presented using other types of statistical features instead of the kurtosis. For this study, the problem of four classes for bearing fault detection is studied using various statistical features. This study is conducted in four stages. At first, the stability of each feature for each fault mode is investigated, then resistance to load change as well as failure growth is studied. At the end, the resolution and fault detection for each feature using the comparison with a determined pattern and the coherence rate is calculated. From the above results, the best feature that is both resistant and repeatable to different variations, as well as the suitable accuracy of detection and resolution, is selected and with comparing to the kurtosis feature, it is found that this feature is not in a good condition in compared with other statistical features such as harmmean and median. The results show that the accuracy of the proposed approach is 100% by using the proposed neural network, even though it uses only two features.
Journal of Mechanical Science and Technology, 2013
This study presents an inverse procedure to identify multiple cracks in beams using an evolutiona... more This study presents an inverse procedure to identify multiple cracks in beams using an evolutionary algorithm. By considering the crack detection procedure as an optimization problem, an objective function can be constructed based on the change of the eigenfrequencies and some strain energy parameters. Each crack is modeled by a rotational spring. The changes in natural frequencies due to the presence of the cracks are related to a damage index vector. Then, the bees algorithm, a swarm-based evolutionary optimization technique, is used to optimize the objective function and find the damage index vector, whose positive components show the number and position of the cracks. A second objective function is also optimized to find the crack depths. Several experimental studies on cracked cantilever beams are conducted to ensure the integrity of the proposed method. The results show that the number of cracks as well as their sizes and locations can be predicted well through this method.
Journal of Adhesion, Apr 20, 2022
Applied and Computational Mechanics, Jun 1, 2021
This paper aims to discuss the vibration analysis of the post-buckled cracked axially functionall... more This paper aims to discuss the vibration analysis of the post-buckled cracked axially functionally graded (AFG) beam. The nonlinear equations of motion of the Euler-Bernoulli beam are derived using the equilibrium principles. Then, these differential equations are converted into a set of algebraic ones using the differential quadrature (DQ) method and solved by an arc-length strategy. The resulted displacement field from the post-buckling analysis is assumed to be the equilibrium state of vibration analysis, and an eigenvalue problem is derived. By solving this linear eigenvalue problem, both the natural frequencies and mode shapes of the beam are calculated. The validation of results in comparison with a similar work shows a good agreement. The effect of several parameters such as the extensible and inextensible clamped-clamped boundary conditions, initial geometric imperfection, crack's depth, and crack's location on the natural frequencies and mode shapes are investigated in detail.
Structural Engineering and Mechanics, 2018
Structural Health Monitoring-an International Journal, Jan 3, 2017
Crack identification in engineering structures has been widely investigated by researchers. Most ... more Crack identification in engineering structures has been widely investigated by researchers. Most of the literature on multiple crack identification, however, has focused on rather simple structures like beams and it is often assumed that the number of cracks is known while this is not a practical assumption. In this article, multiple crack identification in frame structures is investigated based on experimental vibration data using the Bayesian model class selection and swarm-based optimization methods to identify both the number of cracks and their characteristics. To this end, first, the numerical model of the intact frame is updated based on the natural frequencies of the intact state using the particle swarm inspired multi-elitist artificial bee colony algorithm. After updating the intact model of the structure, a set of numerical models of the cracked frame with different numbers of cracks is constructed. Since the number of cracks is not known a priori, the Bayesian model class selection is employed to find the most plausible model class in order to predict the number of cracks. Then, the parameters of the cracks are identified using the particle swarm inspired multi-elitist artificial bee colony algorithm. Instead of pinpointing to one optimal solution obtained after a large number of function evaluations, a set of best solutions whose objective values are less than 10 25 are recorded and the regions where the best solutions are concentrated are identified to see how the solution would differ if less number of function evaluations is employed. To fully assess the effectiveness of this approach, both numerical and experimental examples are utilized. The results confirm the effectiveness of the proposed method for identifying multiple cracks in the frames using a few experimental natural frequencies of the structure. The effect of using more natural frequencies on the accuracy of the location and depth of the cracks is also studied.
Structural and Multidisciplinary Optimization, Feb 27, 2010
... Finite element model updating using bees algorithm Shapour Moradi · Laleh Fatahi · Pejman Raz... more ... Finite element model updating using bees algorithm Shapour Moradi · Laleh Fatahi · Pejman Razi ... Gradient-based tech-S. Moradi (B) · L. Fatahi · P. Razi Mechanical Engineering Department, Shahid Chamran University, Ahvaz, 61355, Iran e-mail: moradis@scu.ac.ir ...
AIAA Journal, 1998
The differential quadrature method (DQM) is used to analyze the one-dimensional buckling of a lam... more The differential quadrature method (DQM) is used to analyze the one-dimensional buckling of a laminated composite beam plate having an across-the-width delamination located at an arbitrary depth and an arbitrary location along its span. A beam theory with shear deformation is used in formulating the problem. Several case studies are conducted to examine the buckling response of laminates hosting such a delamination. Using DQM, the system of equilibrium equations and the boundary conditions are transformed into a system of linear algebraic eigenvalue equations that are solved by a standard eigensolver. The influences of several parameters that affect the buckling strength of such laminates are investigated. The investigated parameters are the shear deformation factor, the length of the delamination, and the through-the-thickness and longitudinal positions of the delamination. The results verify the accuracy and efficiency of DQM.
<jats:title>Abstract</jats:title> <jats:p>In this paper a package is introduced... more <jats:title>Abstract</jats:title> <jats:p>In this paper a package is introduced which handles shape optimization in 2-dimensional elasticity problems where Boundary Element Method is used for the analysis phase affording a large reduction in the problem dimensionality together with a variant of the Method of Center Points for the optimization phase. This optimization method allows a high reduction in the number of constraints considered in each step, as well as low number of cycles, resulting in notable overall efficiency.</jats:p> <jats:p>Design variables in optimum shape determination consists of basic nodal coordinates for B-spline functions as the means to define smooth boundary curves. Maximum stress and/or displacements at critical boundary points are observed as constraints in each cycle of the procedure.</jats:p> <jats:p>Three classical case examples are solved successfully, and the results are compared with those of others, illustrating the superior capabilities of the program package.</jats:p>
WIT transactions on engineering sciences, 1970
In this study the differential quadrature method (DQM) is used to model the postbuckling analysis... more In this study the differential quadrature method (DQM) is used to model the postbuckling analysis of imperfect laminated composite beams having multiple delaminations and subject to axial compressive load. The delaminations are considered to be through-the-width in an arbitrary locations, through-thethickness and along the span of the beam. A nonlinear beam theory is used to formulate the problem. To model the delaminated beam, the beam is divided into a series of regions bounded by the delaminated segments. Using DQM, the system of equilibrium equations and the boundary conditions are transformed into a system of nonlinear algebraic equations that are solved by an arc-length strategy. The contact effect between the delaminated surfaces and the delamination growth due to the opening of the delaminated sections under the compressive load were not considered in this study. To validate the integrity of the DQM, the numerical results obtained from a series of case studies are compared with those of the other published results. These comparisons would confirm the efficiency and accuracy of the DQM.
Mechanical Systems and Signal Processing, Jun 1, 2022
Applied Mechanics and Materials, Nov 1, 2012
This article focuses on the application of the Fourier-expansion based differential quadrature me... more This article focuses on the application of the Fourier-expansion based differential quadrature method (FDQM) for the buckling analysis of ring-stiffened composite laminated cylindrical shells. Displacements and rotations are expressed in terms of Fourier series expansions in longitudinal direction and their first order derivatives are approximated with FDQM in circumferential direction. The &amp;amp;#39;smeared stiffener&amp;amp;#39; approach is adopted for the stiffeners modeling. Two FORTRAN programs prepared for linear and nonlinear analysis and results were compared by ABAQUS finite element software. Buckling loads of stiffened and unstiffened shells considering the effects of changes in shell and stiffener geometric and material properties and also shell lay-ups are investigated.
Applied and Computational Mechanics, Dec 1, 2017
In this study, a hybrid method is proposed to investigate the nonlinear vibrations of pre-and pos... more In this study, a hybrid method is proposed to investigate the nonlinear vibrations of pre-and post-buckled rectangular plates for the first time. This is an answer to an existing need to develop a fast and precise numerical model which can handle the nonlinear vibrations of buckled plates under different boundary conditions and plate shapes. The method uses the differential quadrature element, arc-length, harmonic balance and direct iterative methods. The governing differential equations of plate vibration have been extracted considering shear deformations and the initial geometric imperfection. The solution is assumed to be the sum of the static and dynamic parts which upon inserting them into the governing equations, convert them into two sets of nonlinear differential equations for static and dynamic behaviors of the plate. First, the static solution is calculated using a combination of the differential quadrature element method and an arc-length strategy. Then, putting the first step solutions into the dynamic nonlinear differential equations, the nonlinear frequencies and modal shapes of the plate are extracted using the harmonic balance and direct iterative methods. Comparing the obtained solutions with those published in the literature confirms the accuracy and the precision of the proposed method. The results show that an increase in the nonlinear vibration amplitude increases the nonlinear frequencies.
Applied Mathematical Modelling, Jul 1, 2014
Vibration analysis of cracked post-buckled beam is investigated in this study. Crack, assumed to ... more Vibration analysis of cracked post-buckled beam is investigated in this study. Crack, assumed to be open, is modeled by a massless rotational spring. The beam is divided into two segments and the governing nonlinear equations of motion for the post-buckled state are derived. The solution consists of static and dynamic parts, both leading to nonlinear differential equations. The differential quadrature has been used to solve the problem. First, it is applied to the equilibrium equations, leading to a nonlinear algebraic system of equations that will be solved utilizing an arc length strategy. Next, the differential quadrature is applied to the linearized dynamic differential equations of motion and their corresponding boundary and continuity conditions. Upon solution of the resulting eigenvalue problem, the natural frequencies and mode shapes of the cracked beam are extracted. Several experimental as well as numerical case studies are performed to demonstrate the effectiveness of the proposed method. The investigation also includes an examination of several parameters influencing the dynamic behavior of the problem. The results show that the position and size of the crack as well as the geometric imperfection and applied load largely affect the modal shapes and natural frequencies of the beam.
Journal of Pressure Vessel Technology-transactions of The Asme, Aug 30, 2017
Linearized buckling analysis of functionally graded shells of revolution subjected to displacemen... more Linearized buckling analysis of functionally graded shells of revolution subjected to displacement-dependent pressure, which remains normal to the shell's middle surface throughout the deformation process, is described in this work. Material properties are assumed to be varied continuously in the thickness direction according to a simple power law distribution in terms of the volume fraction of a ceramic and a metal. The governing equations are derived based on the first-order shear deformation theory, which accounts for through the thickness shear flexibility with Sanders type of kinematic nonlinearity. Displacements and rotations in the shell's middle surface are approximated by combining polynomial functions in the meridian direction and truncated Fourier series with an appropriate number of harmonic terms in the circumferential direction. The load stiffness matrix, also known as the pressure stiffness matrix, which accounts for the variation of load direction, is derived for each strip and after assembling resulted in the global load stiffness matrix of the shell, which may be unsymmetric. The load stiffness matrix can be divided into two unsymmetric parts (i.e., load nonuniformity and unconstrained boundary effects) and a symmetric part. The main part of this research is to quantify the effects of these unsymmetries on the follower action of lateral pressure. A detailed numerical study is carried out to assess the influence of various parameters such as power law index of functionally graded material (FGM) and shell geometry interaction with load distribution, and shell boundary conditions on the follower buckling pressure reduction factor. The results indicate that, when applied individually, unconstrained boundary effect and longitudinal nonuniformity of lateral pressure have little effect on the follower buckling reduction factor, but when combined with each other and with circumferentially loading nonuniformity, intensify this effect.
Computational Mechanics, Sep 21, 2000
The application of a robust numerical method, namely the differential quadrature method (DQM) for... more The application of a robust numerical method, namely the differential quadrature method (DQM) for the analysis of buckling and postbuckling of laminated composite plates is introduced. The method is combined with an arc-length strategy to solve the resulting system of nonlinear equations. The treatment accounts for the effect of large deformation by including the von Karman strains. Imperfections in the
Steel and Composite Structures, Jan 20, 2017
International Journal of Pressure Vessels and Piping, Nov 1, 2013
The problem of crack detection in cylindrical shell structures is investigated.> To do this, the ... more The problem of crack detection in cylindrical shell structures is investigated.> To do this, the differential quadrature method and bees algorithm has been used.> Numerical and experimental studies on the cracked free-free shells were conducted.> The results showed that the crack locations, sizes and depths were predicted well.>