Application of various uncertainty measures in the problem of critical force searching for orthotropic shell in conditions of the carrying capacity

The questions of measures calculation of events containing uncertain quantities of random, fuzzy and rough nature are considered. The algorithms of determination of measures of events, based on methods of statistical simulation, are proposed. The "chances" of realization an uncertain event - the simultaneous fulfillment of the conditions of the bearing capacity of a cylindrical orthotropic shell compressed by an axial force, which can be presented in a random, fuzzy or rough manner, are investigated. The stochastic uncertainty is given by the distribution density of the random variable. Fuzzy data are defined by the membership function, and rough data are defined by a deterministic upper and lower approximation. Each type of uncertainty is characterized by its own measures: the probability - for the description of the modality - "probably", the possibility - for the description of the modality is "fuzzy", trust - to describe the modality "rough". The paper proposes procedures for calculating the listed measures. Also numerical illustrations of the calculation of modalities as "probably", "fuzzy", "rough" for the analysis of the limit force of carrying capacity in the problem of optimal design of the compressed orthotropic cylindrical shell made of fiberglass in conditions of uncertainty of the problem of geometrical parameters, such as thickness and radius, and description of the corresponding degree of implementation of an uncertain event are shown. Uncertain event is to fulfill the limitations of general and local stability and durability. The results of the calculations are compared with the solution of the problem with deterministic data. The results show the "reaction" of the values of the critical force to the possible presence of uncertain factors in the problem and the degree of uncertainty. Thus, the bearing capacity of the shell decreases significantly more in the presence of factors of random and rough nature in comparison to the fuzzy data.

Thermomechanical deformation of the orthotropic shell taking into account the deformation anisotropy

A variant of the rotation shell in the particular form of a closed circular cylindrical shell, which is often used in the design practice of civil, power and other industrial structures, is considered. The specificity of the considered shell lies in the features of its material, which has a manifestation of dual anisotropy. In particular, this material is orthotropic in structure, and the nature of deformation shows the dependence of stiffness and strength on the type of stress state. The loading of the shell is assumed to be axisymmetric, taking into account the influence of a medium with variable thermal parameters. The temperature difference between the shell surfaces is taken into account here. The statement of the general thermomechanical problem is carried out in an unrelated form, taking into account a certain independence of the problems of thermodynamics and mechanics. Taking into account the limitations of the classical thermomechanical theories of shells made of materials with dual anisotropy and the fact that the known models for such materials have significant drawbacks, the authors used a variant of the normalized stress space. Differential equations of thermoelasticity for a cylindrical shell are obtained, taking into account the complicated thermomechanical properties of its material. Particular solutions with the features of the results of calculating the shell states are illustrated, and their analysis is carried out.

A Non-Singular Analytical Technique for Reinforced Non-Circular Holes in Orthotropic Laminate

The intricacy in Lekhnitskii’s available single power series solution for stress distribution around hole edge for both circular and noncircular holes represented by a hole shape parameter ε is decoupled by introducing a new technique. Unknown coefficients in the power series in ε are solved by an iterative technique. Full field stress distribution is obtained by following an available method on Fourier solution. The present analytical solution for reinforced square hole in an orthotropic infinite plate is derived by completely eliminating stress singularity that depends on the concept of stress ratio. The region of validity of the present analytical solution on reinforcement area is arrived at based on a comparison with the finite element analysis. The present study will also be useful for deriving analytical solution for orthotropic shell with reinforced noncircular holes.

A three-dimensional biomechanical model for prediction of garment pressure in pressure therapy for burn patients

Compression garments produce a pressure to suppress and flatten hypertrophic scars caused by serious burns, and its value plays a critical role in the treatment. In this study, a 3-D biomechanical mathematical model is established to study numerically the pressure distribution over the arm given by a compression sleeve. The actual geometry of a female arm is used in our study, which is obtained from a 3-D reconstruction of computer X-ray tomography images. The arm model consists of bones and soft tissues, and the sleeve is described by an orthotropic shell model. The finite element method is adopted to predict the pres-sure distribution, which is then experimentally verified in a good agreement, providing a good understanding of the mechanism of pressure action on hypertrophic scars, and enhancing the medical function of a compression garment. The present method offers also a new approach to optimal design of compression garments with real constraints.

PROSPECTS OF ANISOGRID LATTICE STRUCTURES USING IN ADAPTERS OF LAUNCH VEHICLE

The efficiency of using anisogrid lattice structures in launch vehicle designs, in particular in payload adapters, is investigated. On a specific example of the design of the adapter, which is in operation, it is compared with an anisogrid adapter, which is made of different materials - composite, made by winding, and metal using additive technologies. The performance of the adapter was evaluated by the criterion of minimum mass, subject to the requirements of strength and stability. The initial geometric parameters of the anisogrid lattice structure were determined under the condition that the critical stresses are equal for the symmetric and asymmetric cases of stability loss for the structural orthotropic shell model. Calculations and comparisons were made for composite materials - fiberglass, carbon fiber, organoplastic and boraluminium, as well as metal - AMG6M, BT20. Checking the geometrical parameters calculated on the model of structural orthotropic shell showed that they do not meet the requirements of strength and stability. The choice of geometric parameters of a working adapter design is made by numerical experiment with finite element method. The geometry of the lattice structure of the adapter was parameterized to ensure the variability of two geometric dimensions of the cross section of the longitudinal rib and two geometric dimensions of the cross section of the upper frame. The numerical experiment was performed for the constructions made of carbon plastic and for metals AMG6M, BT20. The results of the calculations showed that the anisogrid lattice structures give a gain on the weight of the adapters, which is up to 50% compared to the designs in operation.

Nonlinear Deformation of Flexible Orthotropic Shells of Variable Thickness in an Unsteady Magnetic Field

The analysis of the stress state of a flexible orthotropic shell under the influence of a time-varying mechanical force and a time-varying external electric current is performed, taking into account the mechanical and electromagnetic orthotropy. The effect of thickness on the stress-strain state of the orthotropic shell is investigated. The results obtained indicate the influence of thickness on the deformation of the shell and the need to take this factor into account in the design schemes.

Nonlinear Dynamics of Dacron Aortic Prostheses Conveying Pulsatile Flow

This study addresses the dynamic response to pulsatile physiological blood flow and pressure of a woven Dacron graft currently used in thoracic aortic surgery. The model of the prosthesis assumes a cylindrical orthotropic shell described by means of nonlinear Novozhilov shell theory. The blood flow is modeled as Newtonian pulsatile flow, and unsteady viscous effects are included. Coupled fluid–structure Lagrange equations for open systems with wave propagation subject to pulsatile flow are applied. Physiological waveforms of blood pressure and velocity are approximated with the first eight harmonics of the corresponding Fourier series. Time responses of the prosthetic wall radial displacement are considered for two physiological conditions: at rest (60 bpm) and at high heart rate (180 bpm). While the response at 60 bpm reproduces the behavior of the pulsatile pressure, higher harmonics frequency contributions are observed at 180 bpm altering the shape of the time response. Frequency-responses show resonance peaks for heart rates between 130 bpm and 200 bpm due to higher harmonics of the pulsatile flow excitation. These resonant peaks correspond to unwanted high-frequency radial oscillations of the vessel wall that can compromise the long-term functioning of the prosthesis in case of significant physical activity. Thanks to this study, the dynamic response of Dacron prostheses to pulsatile flow can be understood as well as some possible complications in case of significant physical activity.