Orthotropic Cylindrical Shells Research Articles

Microstructure-based modeling of primary cilia mechanics.

A primary cilium, made of nine microtubule doublets enclosed in a cilium membrane, is a mechanosensing organelle that bends under an external mechanical load and sends an intracellular signal through transmembrane proteins activated by cilium bending. The nine microtubule doublets are the main load-bearing structural component, while the transmembrane proteins on the cilium membrane are the main sensing component. No distinction was made between these two components in all existing models, where the stress calculated from the structural component (nine microtubule doublets) was used to explain the sensing location, which may be totally misleading. For the first time, we developed a microstructure-based primary cilium model by considering these two components separately. First, we refined the analytical solution of bending an orthotropic cylindrical shell for individual microtubule, and obtained excellent agreement between finite element simulations and the theoretical predictions of a microtubule bending as a validation of the structural component in the model. Second, by integrating the cilium membrane with nine microtubule doublets and simulating the tip-anchored optical tweezer experiment on our computational model, we found that the microtubule doublets may twist significantly as the whole cilium bends. Third, besides being cilium-length-dependent, we found the mechanical properties of the cilium are also highly deformation-dependent. More important, we found that the cilium membrane near the base is not under pure in-plane tension or compression as previously thought, but has significant local bending stress. This challenges the traditional model of cilium mechanosensing, indicating that transmembrane proteins may be activated more by membrane curvature than membrane stretching. Finally, we incorporated imaging data of primary cilia into our microstructure-based cilium model, and found that comparing to the ideal model with uniform microtubule length, the imaging-informed model shows the nine microtubule doublets interact more evenly with the cilium membrane, and their contact locations can cause even higher bending curvature in the cilium membrane than near the base.

Vibration of black phosphorus nanotubes via orthotropic cylindrical shell model

Black phosphorus nanotubes (BPNTs) may have good properties and potential applications. Determining the vibration property of BPNTs is essential for gaining insight into the mechanical behaviour of BPNTs and designing optimized nanodevices. In this paper, the mechanical behaviour and vibration property of BPNTs are studied via orthotropic cylindrical shell model and molecular dynamics (MD) simulation. The vibration frequencies of two chiral BPNTs are analysed systematically. According to the results of MD calculations, it is revealed that the natural frequencies of two BPNTs with approximately equal sizes are unequal at each order, and that the natural frequencies of armchair BPNTs are higher than those of zigzag BPNTs. In addition, an armchair BPNTs with a stable structure is considered as the object of research, and the vibration frequencies of BPNTs of different sizes are analysed. When comparing the MD results, it is found that both the isotropic cylindrical shell model and orthotropic cylindrical shell model can better predict the thermal vibration of the lower order modes of the longer BPNTs better. However, for the vibration of shorter and thinner BPNTs, the prediction of the orthotropic cylindrical shell model is obviously superior to the isotropic shell model, thereby further proving the validity of the shell model that considers orthotropic for BPNTs.

A simple SIF determination method for cracked orthotropic cylindrical shell by means of stress ratio

A convenient and universal calculation method for stress intensity factor (SIF) in cracked orthotropic cylindrical shell under diverse loadings is described. The present expressions are derived from traditional classical numerical method and simplified by extracting and eliminating the complex but regular parameters. A simple relation between SIF and crack tip stress from finite element method (FEM) is constructed by means of reference problem and unknown problem, then a simple SIF formulation can be realized and the impact of material orthotropy is considered. The feasibility and advantages of present study are proved to be analyzed by comparing against published results.

FREE VIBRATIONS OF THIN ELASTIC ORTHOTROPIC CYLINDRICAL PANEL WITH RIGID – CLAMPED EDGE GENERATOR

Using the system of equations corresponding to the classical theory of orthotropic cylindrical shells, the free vibrations of thin elastic orthotropic cylindrical panel with rigid – clamped edge generator are investigated. In order to calculate the natural frequencies and to identify the respective natural modes, the generalized Kantorovich-Vlasov method of reduction to ordinary differential equations is used. Dispersion equations for finding the natural frequencies of possible types of vibrations are derived. An asymptotic relation between the dispersion equations of the problem at hand and the analogous problem for a cantilever rectangular plate is established. An algorithm for separating possible boundary vibrations is presented. As an example, the values of dimensionless characteristics of natural frequencies are derived for an orthotropic cylindrical panel.

Thermoelastic State of a Heterogeneous Orthotropic Cylindrical Shell with an Open Profile under Transient Heating

Thermoelastic State of a Heterogeneous Orthotropic Cylindrical Shell with an Open Profile under Transient Heating

Свободные колебания ортотропной цилиндрической оболочки

The paper considers the problem of free oscillations of the orthotropic cylindrical shell of a finite length. This problem was intensively studied in USSR in the second half of the 20th century, but it did not lose its relevance now, for example, works of Dr. Sc. (Eng.) L.G. Gulgazaryan and others should be mentioned. The Corresponding Member of the Academy of Sciences of the USSR Babenko K.I. presented briefly fundamentals of the theory of non-saturable numerical methods in his books. Research in computational mathematics in this area was not sufficiently promoted, and the results remain still practically unknown abroad. At present, actual rediscovery of the those computational methods was started in the West under the "spectral methods" name, as well as in the form of the modern (h--p)-specializations of the finite element method, where the grid was being refined (i.e., for h → 0) simultaneously increasing the degree of polynomials used in approximation of functions within one finite element. Modern algorithm without saturation is presented, and specific calculations are considered showing its high efficiency

Wave Propagation in the Viscoelastic Functionally Graded Cylindrical Shell Based on the First-Order Shear Deformation Theory.

Based on the first-order shear deformation theory (FSDT) and Kelvin-Voigt viscoelastic model, one derives a wave equation of longitudinal guide waves in viscoelastic orthotropic cylindrical shells, which analytically solves the wave equation and explains the intrinsic meaning of the wave propagation. In the numerical examples, the velocity curves of the first few modes for the elastic cylindrical shell are first calculated, and the results of the available literature are compared to verify the derivation and programming. Furthermore, the phase velocity curves and attenuation coefficient curves of the guide waves for a functionally graded (FG) shell are calculated, and the effects of viscoelastic parameters, material gradient patterns, material volume fractions, and size ratios on the phase velocity curves and attenuation curves are studied. This study can be widely used to analytically model the wave propagating in inhomogeneous viscoelastic composite structures and present a theoretical basis for the excellent service performance of composite structures and ultrasonic devices.

Three-dimensional thermoelastic analysis of orthotropic laminated cylindrical shells subjected to uniformly localized thermal boundary conditions

Accurate evaluation of three-dimensional (3D) thermal-elastic analysis of laminated cylindrical shells under different loads has a significant impact on their safety design. In this study, we present a 3D thermoelastic solution of laminated orthotropic cylindrical shells subjected to uniformly localized thermal boundary conditions. For a homogeneous orthotropic layer, a thinning layer approach is introduced to deal with the heat conduction equation and the elastic equation. Based on the eigenequation method and pseudo-Stroh formalism, general solutions for physical quantities of a homogeneous layer are derived. The propagator matrix method is used to deal with multilayered media. A closed form solution for the laminated cylindrical shells is obtained. A numerical example of a 3-layered cylindrical shell subjected to convective heat transfer boundary conditions is presented to verify the solutions’ correctness. An excellent convergence of the current approach is found and the physical quantities predicted by the current method agree well with the numerical results by the finite element method. Finally, the numerical solutions of a 3-layered orthotropic cylindrical shell subjected to uniformly localized thermal boundary conditions are obtained by the current method. The closed form solution presented in this article can be used for 3D thermoelastic analysis of laminated cylindrical shells under complex boundary conditions.

Buckling analysis of an orthotropic cylindrical shell structure in the ANSYS Mechanical APDL software package

Buckling analysis of an orthotropic cylindrical shell structure in the ANSYS Mechanical APDL software package

Flügge shell theory and solution for the vibration analysis of a thin elastic cylindrical panel of varying curvature

In this paper, the free vibration behavior of isotropic and orthotropic cylindrical shell panels with variable curvature subjected to certain ends boundary conditions is analyzed by the transfer matrix technique and solved by the Romberg integration approach. Flügge’s shell theory is employed to model the governing three-dimensional equations of vibration and Fourier’s approach is used to deform the displacement fields as trigonometric functions in the longitudinal direction. As a result of a semi-analytical procedure is conducted, the coupled governing equations of panel problem can be written in a matrix partial differential equation of first order with variable coefficients and reduced from the two-dimensional problem to one-dimensional one which is solved numerically as an initial-value problem. The proposed model is applied to get the natural frequencies and mode shapes for the vibration behavior of two-side simply-supported cylindrical panels with simply-supported, free-free, clamped-free and clamped-clamped ends boundary conditions lying at their curved edges. The sensitivity of the vibration behavior to the variety of curvature, panel parameters and material orthotropy of shell is studied.

Determination and analysis of the thermoelastic state of layered orthotropic cylindrical shells

The fundamental relations of the quasi-static problem of thermoelasticity are written for a finite layered orthotropic cylindrical shell of an antisymmetric structure. Under convective heat transfer on the surfaces of this shell and under a linear dependence of temperature on the transverse coordinate, the basic system of equations for the integral characteristics of temperature is given. The method is proposed for solving the formulated problems of thermoelasticity and thermal conductivity, using the double finite integral Fourier transform with respect to the corresponding coordinates of the transformation and Laplace transform with respect to the time. The results of a numerical analysis of temperature, deflections, and stresses for the considered two-layer shell hinged at the edges under local heating by the initially specified temperature field are presented.

Parametric vibrations of a viscous-elastic medium-contacting, damaged, orthotropic cylindrical shell stiffened with inhomogeneous rods

Parametric vibrations of a viscous-elastic medium-contacting, damaged, orthotropic cylindrical shell stiffened with inhomogeneous rods

Thermal stresses in the orthotropic cylindrical shell of irregular layered structure

Thermal stresses in the orthotropic cylindrical shell of irregular layered structure

Buckling of a Composite Cylindrical Shell with Cantilever-like Boundary Conditions under Hydrostatic Pressure

In this study, an analytical solution for the buckling of a composite cylindrical shell subjected to hydrostatic pressure is proposed. The boundary conditions of the composite cylindrical shell are cantilever-like, with one end fixed and the other end connected to a rigid disk. The differential equations are solved using the Galerkin method. The axial displacement of the shell is approximated by the first mode shape of the transverse vibration of the clamped sliding beam. The circumferential displacement and deflection are approximated by the first derivation of the beam function. Based on this solution, an analytical formula enabling prediction of the critical buckling pressure and buckling mode of composite orthotropic cylindrical shells is derived. A finite element analysis and external hydrostatic pressure test are conducted to verify the proposed approach. The efficiency and accuracy of the analytical solution in predicting the critical buckling pressure and buckling mode are demonstrated.

Reliability evaluation of critical local buckling load on the thin walled cylindrical shell made of composite material

The goal of this research is to evaluate the variability of the buckling load in thin orthotropic cylindrical shells due to the deviation with respect to the nominal values, for both the geometrical and material properties. In this research also the fiber orientation i.e the alignment with respect to the cylinder axis was considered. The research is developed by comparing the results obtained through analytical formulas and numerical results (f.e.m.) for isotropic and orthotropic materials. The coefficient of variation for critical buckling load (for symmetrical and non-symmetrical deformation), assumed for comparing the standard deviation values, is linear with the variation of material and geometrical parameters. The standard deviation on critical buckling load considering both the material and geometrical variations and fiber orientation can be very well described by a surface. From these surfaces it is important to underline that to quantify the dispersion values on the critical buckling load, the material properties assume the fundamental role with respect to the fiber orientation. The main implications of these results are correlated to the fact that, for example, during the manufacturing process, the geometrical and material variability is more important than the fiber orientation in order to have a reliability component.

Nonlinear Parametric Oscillations of a Longitudinally Reinforced Orthotropic Cylindrical Shell Filled with a Viscous Liquid

Nonlinear Parametric Oscillations of a Longitudinally Reinforced Orthotropic Cylindrical Shell Filled with a Viscous Liquid

A symplectic analytical approach for free vibration of orthotropic cylindrical shells with stepped thickness under arbitrary boundary conditions

Exact analytical solutions for free vibration of isotropic and orthotropic cylindrical shells with uniform and stepped thickness subject to general boundary conditions are presented by means of a symplectic analytical approach. The Reissner shell theory is adopted to formulate a theoretical model. By introducing a Hamiltonian system, the governing higher order partial differential equation is reduced to a set of ordinary differential equations which can be analytically solved by separating the variables. Applying the end boundary and interface continuous conditions, a set of analytical characteristic frequency equations are obtained, and exact solutions can be determined. To ensure accuracy and validity of the symplectic method, the analytical solutions for uniform and stepped cylindrical shells with isotropic or orthotropic material properties and with arbitrary boundary conditions are compared with available published data and FEM solution. A set of comprehensive new result for orthotropic stepped cylindrical shells under classical and elastic restraints are presented. Some typical mode shapes for various examples are illustrated. In addition, the effects of boundary conditions and orthotropic properties on vibration frequency are analyzed. The result shows that the fundamental frequency is higher for a boundary with more constraints.

Symbolic homogenization and structure optimization for a periodically perforated cylindrical shell

AbstractThe main focus of this paper lies in the drastic model reduction for a complex multi‐scale problem of linear elasticity. The core of the work lies in the structural optimization of periodic perforated cylindrical shells under a given load on a small portion of the surface. Periodic structure of the shell is a frame of beams. Algorithm presented in the paper utilizes two our recent analysis works on homogenization and dimension reduction of the problem in the perforated 3D shell to two‐dimensional homogenized shell, and then dimension reduction w.r.t. the beam thickness in auxiliary cell‐problems to problem on a frame of beams, by asymptotic method. In this paper, we found the analytical solution for the orthotropic cylindrical shell, obtained in the limit, by variable separation and Fourier analysis. The solution depends explicitly on the effective properties, which are computed symbolically, and on the design variables of the structure. Cell‐problems are solved by symbolic means and the structural design for this type of the loading has been optimized. Moreover, this yields a semi‐analytic optimization problem and the practical usage of the underlying theoretical derivation. We stress that the homogenization and dimension reduction of a shell with holes and the analytic solution to the corresponding macroscopic problem are new.

Semi-analytical solutions for buckling and free vibration of composite anisogrid lattice cylindrical panels

In this study, highly accurate approximate closed-form solution is presented for buckling and free vibration of clamped composite anisogrid lattice cylindrical panels. Using theory of orthotropic cylindrical shallow shells based on the continuous model of lattice structures, the system of governing partial differential equations (PDEs) of motion is derived. The resulted PDEs are converted to a couple of systems of ordinary differential equations (ODEs) by employing of the Extended Kantorovich Method (EKM). Semi-analytical solutions are presented for both buckling and free vibration of anisogrid lattice panels via iterative application of infinite power series solution for the sets of ODEs. Efficiency of the presented method in terms of accuracy, stability, fast convergence and low computational cost for prediction of the critical buckling loads and natural frequencies are examined. Accuracy of the predictions for various cases are studied by comparing with available numerical and analytical results. Moreover, it is shown that the method can be used to obtain accurate solutions for buckling and free vibration of composite lattice rectangular plates by assuming large values for the radius together with small values for the angle of the panel. This implies stability of the method for large or small values while providing accurate predictions.

Exact benchmark solutions of random vibration responses for thin-walled orthotropic cylindrical shells

The exact solutions of random vibration responses of orthotropic thin cylindrical shells are imperative for verifying numerical approaches. This study proposes the discrete analytical method (DAM) and achieves the exact benchmark responses of thin-walled orthotropic cylindrical shells under stationary and nonstationary random excitations for the first time. Firstly, by revisiting the governing motion equations of elastic orthotropic shells based on the Flügge shell theory, the closed-form modal shape functions of orthotropic cylindrical shell with shear diaphragm boundary condition are introduced into stationary and nonstationary random vibration analyses. The power spectral density functions and root mean squares (RMSs) for stochastic responses of thin shell subjected to various random excitations, including the point, surface, base acceleration and moving excitations, are analytically derived by using the pseudo excitation method. Moreover, DAM is proposed to enhance the computational efficiency by implementing the discretization of the modal coordinates, frequency and temporal domains. Finally, the exact benchmark solutions of stationary and nonstationary stochastic responses are achieved, and the results indicate high accuracy and efficiency of proposed DAM. The excitation bandwidth and spatial distribution have significantly different effects on various types of responses, and maximum response RMS declines with increasing of acceleration of moving load.