The Experts below are selected from a list of 15555 Experts worldwide ranked by ideXlab platform
Abdullah H. Sofiyev - One of the best experts on this subject based on the ideXlab platform.
-
Large-amplitude vibration of the geometrically imperfect FGM truncated conical shell
Journal of Vibration and Control, 2015Co-Authors: Abdullah H. Sofiyev, N KuruogluAbstract:In this study, the Large-amplitude vibration of a functionally graded (FG) truncated conical shell with an initial geometric imperfection has been investigated using Large Deformation Theory with a von Karman–Donnell type of kinematic nonlinearity. The material properties of an FG truncated conical shell are assumed to vary continuously through the thickness. The fundamental relations, the modified Donnell-type nonlinear motion, and compatibility equations of the FG truncated conical shell with an initial geometric imperfection are derived. The relation between nonlinear frequency parameters with the dimensionless amplitude of imperfect FG truncated conical shells is obtained. Finally, the influences of variations of the initial geometric imperfection, compositional profiles, and shell characteristics on the dimensionless nonlinear frequency parameter and frequency–amplitude relations are investigated. The present results are compared with the available data for a special case.
-
the influence of non homogeneity on the frequency amplitude characteristics of laminated orthotropic truncated conical shell
Composite Structures, 2014Co-Authors: Abdullah H. SofiyevAbstract:Abstract In this study, the non-linear vibration of laminated non-homogenous orthotropic truncated conical shell is investigated. It is assumed that the Young’s moduli, shear modulus and density of the layers of the shell vary exponentially through the thickness direction. The basic equations of laminated non-homogenous orthotropic truncated conical shells are derived using the Large Deformation Theory with von Karman–Donnell-type of kinematic non-linearity. The non-linear basic equations are reduced to the non-linear differential equation depending on the time using the superposition principle and Galerkin method. This equation is solved using semi-inverse method and is found the frequency–amplitude relationship. Finally, carrying out some computations, the effects of non-homogeneity, number and ordering of layers, and conical shell characteristics on frequency–amplitude characteristics have been studied.
-
non linear buckling of an fgm truncated conical shell surrounded by an elastic medium
International Journal of Pressure Vessels and Piping, 2013Co-Authors: Abdullah H. Sofiyev, N KuruogluAbstract:Abstract In this paper, the non-linear buckling of the truncated conical shell made of functionally graded materials (FGMs) surrounded by an elastic medium has been studied using the Large Deformation Theory with von Karman–Donnell-type of kinematic non-linearity. A two-parameter foundation model (Pasternak-type) is used to describe the shell–foundation interaction. The FGM properties are assumed to vary continuously through the thickness direction. The fundamental relations, the modified Donnell type non-linear stability and compatibility equations of the FGM truncated conical shell resting on the Pasternak-type elastic foundation are derived. By using the Superposition and Galerkin methods, the non-linear stability equations for the FGM truncated conical shell is solved. Finally, influences of variations of Winkler foundation stiffness and shear subgrade modulus of the foundation, compositional profiles and shell characteristics on the dimensionless critical non-linear axial load are investigated. The present results are compared with the available data for a special case.
-
the effect of non homogeneity on the non linear buckling behavior of laminated orthotropic conical shells
Composites Part B-engineering, 2012Co-Authors: Abdullah H. Sofiyev, N Kuruoglu, A M NajafovAbstract:Abstract In this work, the buckling behavior of the cross-ply laminated non-homogeneous orthotropic truncated conical shells in the Large Deformation under the uniform axial load is studied. Firstly, the basic relations of the cross-ply laminated non-homogeneous orthotropic truncated conical shells are derived using the Large Deformation Theory. Then modified Donnell type non-linear stability and compatibility equations are obtained and solved. A computer program called Maple 14 has been used in the numerical solution. Finally, the influences of the degree of non-homogeneity, the number and ordering of layers and the variations of the conical shell characteristics on the non-linear axial buckling load are investigated. The comparison with available results is satisfactorily good.
-
non linear buckling behavior of fgm truncated conical shells subjected to axial load
International Journal of Non-linear Mechanics, 2011Co-Authors: Abdullah H. SofiyevAbstract:Abstract In this study, the non-linear buckling behavior of truncated conical shells made of functionally graded materials (FGMs), subject to a uniform axial compressive load, has been investigated using the Large Deformation Theory with von the Karman–Donnell-type of kinematic non-linearity. The material properties of functionally graded shells are assumed to vary continuously through the thickness of the shell. The variation of properties followed an arbitrary distribution in terms of the volume fractions of the constituents. The fundamental relations, the modified Donnell type non-linear stability and compatibility equations of functionally graded truncated conical shells are obtained and are solved by superposition and Galerkin methods and the upper and lower critical axial loads have been found analytically. Finally, the influences of the compositional profile variations and the variation of the shell geometry on the upper and lower critical axial loads are investigated. Comparing the results of this study with those in the literature validates the present analysis.
N Kuruoglu - One of the best experts on this subject based on the ideXlab platform.
-
Large-amplitude vibration of the geometrically imperfect FGM truncated conical shell
Journal of Vibration and Control, 2015Co-Authors: Abdullah H. Sofiyev, N KuruogluAbstract:In this study, the Large-amplitude vibration of a functionally graded (FG) truncated conical shell with an initial geometric imperfection has been investigated using Large Deformation Theory with a von Karman–Donnell type of kinematic nonlinearity. The material properties of an FG truncated conical shell are assumed to vary continuously through the thickness. The fundamental relations, the modified Donnell-type nonlinear motion, and compatibility equations of the FG truncated conical shell with an initial geometric imperfection are derived. The relation between nonlinear frequency parameters with the dimensionless amplitude of imperfect FG truncated conical shells is obtained. Finally, the influences of variations of the initial geometric imperfection, compositional profiles, and shell characteristics on the dimensionless nonlinear frequency parameter and frequency–amplitude relations are investigated. The present results are compared with the available data for a special case.
-
non linear buckling of an fgm truncated conical shell surrounded by an elastic medium
International Journal of Pressure Vessels and Piping, 2013Co-Authors: Abdullah H. Sofiyev, N KuruogluAbstract:Abstract In this paper, the non-linear buckling of the truncated conical shell made of functionally graded materials (FGMs) surrounded by an elastic medium has been studied using the Large Deformation Theory with von Karman–Donnell-type of kinematic non-linearity. A two-parameter foundation model (Pasternak-type) is used to describe the shell–foundation interaction. The FGM properties are assumed to vary continuously through the thickness direction. The fundamental relations, the modified Donnell type non-linear stability and compatibility equations of the FGM truncated conical shell resting on the Pasternak-type elastic foundation are derived. By using the Superposition and Galerkin methods, the non-linear stability equations for the FGM truncated conical shell is solved. Finally, influences of variations of Winkler foundation stiffness and shear subgrade modulus of the foundation, compositional profiles and shell characteristics on the dimensionless critical non-linear axial load are investigated. The present results are compared with the available data for a special case.
-
the effect of non homogeneity on the non linear buckling behavior of laminated orthotropic conical shells
Composites Part B-engineering, 2012Co-Authors: Abdullah H. Sofiyev, N Kuruoglu, A M NajafovAbstract:Abstract In this work, the buckling behavior of the cross-ply laminated non-homogeneous orthotropic truncated conical shells in the Large Deformation under the uniform axial load is studied. Firstly, the basic relations of the cross-ply laminated non-homogeneous orthotropic truncated conical shells are derived using the Large Deformation Theory. Then modified Donnell type non-linear stability and compatibility equations are obtained and solved. A computer program called Maple 14 has been used in the numerical solution. Finally, the influences of the degree of non-homogeneity, the number and ordering of layers and the variations of the conical shell characteristics on the non-linear axial buckling load are investigated. The comparison with available results is satisfactorily good.
Lallit Anand - One of the best experts on this subject based on the ideXlab platform.
-
a thermo mechanically coupled Large Deformation Theory for amorphous polymers in a temperature range which spans their glass transition
International Journal of Plasticity, 2010Co-Authors: Vikas Srivastava, Shawn A Chester, Nicoli M Ames, Lallit AnandAbstract:Abstract Amorphous thermoplastic polymers are important engineering materials; however, their non-linear, strongly temperature- and rate-dependent elastic-viscoplastic behavior is still not very well understood, and is modeled by existing constitutive theories with varying degrees of success. There is no generally agreed upon Theory to model the Large-Deformation, thermo-mechanically-coupled, elastic-viscoplastic response of these materials in a temperature range which spans their glass transition temperature. Such a Theory is crucial for the development of a numerical capability for the simulation and design of important polymer processing operations, and also for predicting the relationship between processing methods and the subsequent mechanical properties of polymeric products. In this paper we extend our recently published Theory [Anand, L., Ames, N. M., Srivastava, V., Chester, S. A., 2009. A thermo-mechanically-coupled Theory for Large Deformations of amorphous polymers. Part I: formulation. International Journal Plasticity 25, 1474–1494; Ames, N. M., Srivastava, V., Chester, S. A., Anand, L., 2009. A thermo-mechanically coupled Theory for Large Deformations of amorphous polymers. Part II: applications. International Journal of Plasticity 25, 1495–1539] to fill this need. We have conducted Large strain compression experiments on three representative amorphous polymeric materials – a cyclo-olefin polymer (Zeonex-690R), polycarbonate (PC), and poly(methyl methacrylate) (PMMA) – in a temperature range from room temperature to approximately 50 °C above the glass transition temperature, ϑ g , of each material, in a strain-rate range of ≈ 10 - 4 to 10 - 1 s - 1 , and compressive true strains exceeding 100%. We have specialized our constitutive Theory to capture the major features of the thermo-mechanical response of the three materials studied experimentally. We have numerically implemented our thermo-mechanically-coupled constitutive Theory by writing a user material subroutine for a widely used finite element program. In order to validate the predictive capabilities of our Theory and its numerical implementation, we have performed the following validation experiments: (i) a plane-strain forging of PC at a temperature below ϑ g , and another at a temperature above ϑ g ; (ii) blow-forming of thin-walled semi-spherical shapes of PC above ϑ g ; and (iii) microscale hot-embossing of channels in Zeonex and PMMA above ϑ g . By comparing the results from this suite of validation experiments of some key features, such as the experimentally-measured deformed shapes and the load-displacement curves, against corresponding results from numerical simulations, we show that our Theory is capable of reasonably accurately reproducing the experimental results obtained in the validation experiments.
-
the mechanics and thermodynamics of continua
2010Co-Authors: Morton E Gurtin, Eliot Fried, Lallit AnandAbstract:Part I. Vector and Tensor Algebra Part II. Vector and Tensor Analysis Part III. Kinematics Part IV. Basic Mechanical Principles Part V. Basic Thermodynamical Principles Part VI. Mechanical and Thermodynamical Laws at a Shock Wave Part VII. Basic Requirements for Developing Physically Meaningful Constitutive Theories Part VIII. Rigid Heat Conductors Part IX. The Mechanical Theory of Compressible and Incompressible Fluids Part X. Mechanical Theory of Elastic Solids Part XI. Thermoelasticity Part XII. Species Diffusion Coupled to Elasticity Part XIII. Theory of Isotropic Plastic Solids Undergoing Small Deformations Part XIV. Small Deformation, Isotropic Plasticity Based on the Principle of Virtual Power Part XV. Small Deformation, Isotropic Plasticity Based on the Principle of Virtual Power Part XVI. Large-Deformation Theory of Isotropic Plastic Solids Part XVII. Theory of Single Crystals Undergoing Small Deformations Part XVIII. Single Crystals Undergoing Large Deformations.
-
a Large Deformation Theory for rate dependent elastic plastic materials with combined isotropic and kinematic hardening
International Journal of Plasticity, 2009Co-Authors: David L Henann, Lallit AnandAbstract:Abstract We have developed a Large Deformation viscoplasticity Theory with combined isotropic and kinematic hardening based on the dual decompositions F = F e F p [Kroner, E., 1960. Allgemeine kontinuumstheorie der versetzungen und eigenspannungen. Archive for Rational Mechanics and Analysis 4, 273–334] and F p = F en p F dis p [Lion, A., 2000. Constitutive modelling in finite thermoviscoplasticity: a physical approach based on nonlinear rheological models. International Journal of Plasticity 16, 469–494]. The elastic distortion F e contributes to a standard elastic free-energy ψ ( e ) , while F en p , the energetic part of F p , contributes to a defect energy ψ ( p ) – these two additive contributions to the total free energy in turn lead to the standard Cauchy stress and a back-stress. Since F e = FF p - 1 and F en p = F p F dis p - 1 , the evolution of the Cauchy stress and the back-stress in a Deformation-driven problem is governed by evolution equations for F p and F dis p – the two flow rules of the Theory. We have also developed a simple, stable, semi-implicit time-integration procedure for the constitutive Theory for implementation in displacement-based finite element programs. The procedure that we develop is “simple” in the sense that it only involves the solution of one non-linear equation, rather than a system of non-linear equations. We show that our time-integration procedure is stable for relatively Large time steps, is first-order accurate, and is objective.
-
a Large Deformation strain gradient Theory for isotropic viscoplastic materials
International Journal of Plasticity, 2009Co-Authors: S P Lele, Lallit AnandAbstract:Abstract This study develops a thermodynamically consistent Large-Deformation Theory of strain-gradient viscoplasticity for isotropic materials based on: (i) a scalar and a vector microstress consistent with a microforce balance; (ii) a mechanical version of the two laws of thermodynamics for isothermal conditions, that includes via the microstresses the work performed during viscoplastic flow; and (iii) a constitutive Theory that allows: • the free energy to depend on ∇ γ p , the gradient of equivalent plastic strain γ p , and this leads to the vector microstress having an energetic component; • strain-hardening dependent on the equivalent plastic strain γ p , and a scalar measure ϕ p related to the accumulation of geometrically necessary dislocations; and • a dissipative part of the vector microstress to depend on ∇ ν p , the gradient of the equivalent plastic strain rate. The microscopic force balance, when augmented by constitutive relations for the microscopic stresses, results in a nonlocal flow rule in the form of a second-order partial differential equation for the equivalent plastic strain γ p . In general, the flow rule, being nonlocal, requires microscopic boundary conditions. However, for problems which do not involve boundary conditions on γ p , and for situations in which the dissipative part of the microstress may be neglected, the nonlocal flow rule may be inverted to give an equation for the plastic strain rate in the conventional form, but with additional gradient-dependent strengthening terms. For such special circumstances the Theory may be relatively easily implemented by writing a user-material subroutine for standard finite element programs. We have implemented such a two-dimensional finite Deformation plane–strain Theory, and using this numerical capability we here report on our studies concerning: (a) the gradient-stabilization of shear band widths in problems which exhibit shear localization; (b) strengthening in pure bending due to strain-gradient effects; and (c) the well-known size-effect regarding hardness versus indentation depth in nano/micro-indentation experiments.
A M Najafov - One of the best experts on this subject based on the ideXlab platform.
-
the effect of non homogeneity on the non linear buckling behavior of laminated orthotropic conical shells
Composites Part B-engineering, 2012Co-Authors: Abdullah H. Sofiyev, N Kuruoglu, A M NajafovAbstract:Abstract In this work, the buckling behavior of the cross-ply laminated non-homogeneous orthotropic truncated conical shells in the Large Deformation under the uniform axial load is studied. Firstly, the basic relations of the cross-ply laminated non-homogeneous orthotropic truncated conical shells are derived using the Large Deformation Theory. Then modified Donnell type non-linear stability and compatibility equations are obtained and solved. A computer program called Maple 14 has been used in the numerical solution. Finally, the influences of the degree of non-homogeneity, the number and ordering of layers and the variations of the conical shell characteristics on the non-linear axial buckling load are investigated. The comparison with available results is satisfactorily good.
Guo Yao - One of the best experts on this subject based on the ideXlab platform.
-
chaotic motion of a composite laminated plate with geometric nonlinearity in subsonic flow
International Journal of Non-linear Mechanics, 2013Co-Authors: Guo YaoAbstract:Abstract The bifurcation and chaotic motion of a two-dimensional (2D) composite laminated plate with geometric nonlinearity subjected to incompressible subsonic flow and transverse harmonic excitation is investigated. Based on von Karman's Large Deformation Theory and incompressible subsonic aerodynamic model, the equation of motion of the composite laminated plate is established using the Hamilton's principle. The variable separation method is adopted to transform the equation of motion of the laminated plate into nonlinear ordinary differential equations (ODE). For the first-order expansion of the transverse displacement, the critical divergence velocity corresponding to the pitchfork bifurcation of the laminated plate is obtained by analyzing the stiffness term in the nonlinear ODE and the Melnikov's method is adopted to predict the chaotic motion of the plate after the bifurcation. The effects of the flow velocity and the amplitude and angular frequency of the external excitation on the chaotic motion of the plate are analyzed. Numerical simulations of the transverse displacement–time history, phase portrait, Poincare map and bifurcation diagrams of the transverse displacement are used to verify the validity of the analytical results. For higher-order expansion of the transverse displacement, the critical divergence velocity is obtained by analyzing the stiffness matrix in the ODEs. The displacement–time histories and phase portraits of the transverse displacement obtained from higher-order expansions are compared with those obtained from the first-order expansion. The effects of the ply angles of the laminated plate on the critical divergence velocity are also discussed for both the first-order expansion and higher-order expansion of the transverse displacement. It can be seen from the results that the critical divergence velocity of the laminated plate decreases with the increasing ply angle. The parameters of the flow velocity and the amplitude and angular frequency of the external excitation for generating the chaotic motion of the plate obtained by the numerical simulations are within the range predicted by the Melnikov's method. Comparing with the results obtained by the higher-order expansions of the displacement, the first-order expansion can qualitatively reflect the dynamic characteristics of the composite laminated plate in subsonic flow.
