scholarly journals Visualization of the Process of Static Buckling of a Micropolar Meshed Cylindrical Panel

2020 ◽  
pp. short10-1-short10-9
Author(s):  
Ekaterina Krylova ◽  
Irina Papkova ◽  
Vadim Krysko
Keyword(s):  
Geometric Nonlinearity ◽  
Scale Effects ◽  
Stability Loss ◽  
Static Stability ◽  
Cylindrical Panel ◽  
Micropolar Theory ◽  
Mesh Structure ◽  
Process Visualization ◽  
The Mathematical Model ◽  
Model Visualization

Process visualization of static stability loss in mechanics is shown by the micropolar meshed cylindrical panel example with two families of mutually perpendicular ribs. The mathematical model of the panel's behavior is based on the Kirchhoff-Love hypotheses. The micropolar theory is applied to ac-count for scale effects. Geometric nonlinearity is taken into account according to the theory of Theodor von Karman. The mesh structure is taken into account based on the Pshenichnov I. G. continuum model. Visualization of numerical results using Autodesk 3ds Max software made it possible to more clearly assess the phenomenon of static buckling of the shell in question. Visualization of the results using 3D made it possible to establish that an in-crease in the distance between the edges of the mesh panel and an increase in the parameter depending on the size does not change the bending shape of the panel, as well as the diagrams of moments and forces at subcritical and supercritical loads.

scholarly journals Torsional Characteristics of Carbon Nanotubes: Micropolar Elasticity Models and Molecular Dynamics Simulation

Nanomaterials ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 453
Author(s):  
Razie Izadi ◽  
Meral Tuna ◽  
Patrizia Trovalusci ◽  
Esmaeal Ghavanloo
Keyword(s):  
Carbon Nanotubes ◽  
Molecular Dynamics ◽  
Scale Effects ◽  
Couple Stress Theory ◽  
Dynamics Simulation ◽  
Local Theory ◽  
Beam Model ◽  
Specific Class ◽  
Micropolar Theory ◽  
Material Parameters

Efficient application of carbon nanotubes (CNTs) in nano-devices and nano-materials requires comprehensive understanding of their mechanical properties. As observations suggest size dependent behaviour, non-classical theories preserving the memory of body’s internal structure via additional material parameters offer great potential when a continuum modelling is to be preferred. In the present study, micropolar theory of elasticity is adopted due to its peculiar character allowing for incorporation of scale effects through additional kinematic descriptors and work-conjugated stress measures. An optimisation approach is presented to provide unified material parameters for two specific class of single-walled carbon nanotubes (e.g., armchair and zigzag) by minimizing the difference between the apparent shear modulus obtained from molecular dynamics (MD) simulation and micropolar beam model considering both solid and tubular cross-sections. The results clearly reveal that micropolar theory is more suitable compared to internally constraint couple stress theory, due to the essentiality of having skew-symmetric stress and strain measures, as well as to the classical local theory (Cauchy of Grade 1), which cannot accounts for scale effects. To the best of authors’ knowledge, this is the first time that unified material parameters of CNTs are derived through a combined MD-micropolar continuum theory.

Walking Stability Analysis of Multi-Legged Crablike Robot over Slope

2013 ◽  
Vol 572 ◽  
pp. 636-639
Author(s):  
Xi Chen ◽  
Gang Wang
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Stability Criterion ◽  
Stability Margin ◽  
Static Stability ◽  
Matlab Simulation ◽  
And Performance ◽  
The Stability ◽  
The Mathematical Model ◽  
The Relationship

This paper deals with the walking stability analysis of a multi-legged crablike robot over slope using normalized energy stability margin (NESM) method in order to develop a common stabilization description method and achieve robust locomotion for the robot over rough terrains. The robot is simplified with its static stability being described by NESM. The mathematical model of static stability margin is built so as to carry out the simulation of walking stability over slope for the crablike robot that walks in double tetrapod gait. As a consequence, the relationship between stability margin and the height of the robots centroid, as well as its inclination relative to the ground is calculated by the stability criterion. The success and performance of the stability criterion proposed is verified through MATLAB simulation and real-world experiments using multi-legged crablike robot.

scholarly journals WAVE ATTENUATION AND WAVE SET-UP ON A COASTAL REEF

1980 ◽  
Vol 1 (17) ◽  
pp. 27 ◽  
Author(s):  
Franciscus Gerritsen
Keyword(s):  
Mathematical Model ◽  
Wave Attenuation ◽  
Scale Effects ◽  
Shallow Reef ◽  
Laboratory Investigations ◽  
Deep Water Wave ◽  
Set Up ◽  
The University ◽  
Incident Waves ◽  
The Mathematical Model

In attempting to specify criteria for the design of structures on coastal reefs, it was found that no adequate method existed to derive those criteria from the deep water wave conditions. In order to fill the gap, a program of measurements and analysis was initiated at the University of Hawaii. The program consisted of prototype and laboratory measurements. Great emphasis was placed on reliable field data, which were collected on Ala Moana Reef, in Honolulu. Laboratory investigations on the behavior of waves on shallow reefs are subject to scale effects; verification from field observations is required to obtain reliable results. As a result of this study, a mathematical model was developed for the calculation of wave attenuation and wave set-up on a shallow reef, using the incident waves in the ocean as boundary conditions. This paper discusses the general behavior of waves approaching a shallow reef and presents some essential characteristics of the mathematical model. The study is limited to waves approaching the shoreline at right angles. The results of this study can be extended to breakwaters with wide, submerged berms.

scholarly journals THE STUDY OF THE AUTONOMOUS SYNCHRONOUS GENERATOR MODES

2017 ◽  
Vol 60 (5) ◽  
pp. 433-445
Author(s):  
V. S. Safaryan
Keyword(s):  
Mathematical Model ◽  
Angular Velocity ◽  
Power System ◽  
Synchronous Generator ◽  
Transition Process ◽  
Static Stability ◽  
Stationary Points ◽  
Natural Form ◽  
Fourth Degree ◽  
The Mathematical Model

The importance of the problem of the static stability of the stationary mode of the power system for its operation is extremely high. The investigation of the static stability of the power system is a subject of a number of works, but the problems of static stability of the stationary points of an autonomous synchronous generator are given little attention. The article considers transient and resonant (stationary) modes of the generator under active-inductive and active-capacitive loads. Mathematical model of transients in a natural form and in the coordinate system d, q are plotted. It is discovered that the mathematical model of the transition process of an autonomous synchronous generator is identical to the mathematical model of the transition process of the synchronous machine under three-phase short circuit. Electromagnetic transients of an autonomous synchronous generator are described by a system of linear autonomous differential equations with constant coefficients. However, the equivalent circuit of a generator contains dependent sources. We investigated the stability of stationary motion of an autonomous synchronous generator at a given angular velocity of rotation of the rotor. The condition for the existence and stability of stationary points of an autonomous synchronous generator is derived. The condition for the existence of stationary points of such a generator does not depend on the active load resistance and stator windings, and inductance of the rotor. The determining of stationary points of the generator is reduced to finding roots of a polynomial of the fourth degree. The graphs of electromagnetic torque dependencies on the angular velocity of rotation of the rotor (mechanical characteristics) are plotted. The equivalent circuits, corresponding to the equations of the transition process of an autonomous synchronous generator, are featured as well.

scholarly journals METHODOLOGY RESEARCH OF STABILITY OF SHALLOW ORTHOTROPIC SHELLS OF DOUBLE CURVATURE UNDER DYNAMIC LOADING

2017 ◽  
Vol 13 (2) ◽  
pp. 145-153
Author(s):  
Alexey A. Semenov
Keyword(s):  
Mathematical Model ◽  
Carbon Fiber ◽  
Dynamic Loading ◽  
Transverse Shear ◽  
Critical Loads ◽  
Geometric Nonlinearity ◽  
Double Curvature ◽  
Ode System ◽  
Orthotropic Shells ◽  
The Mathematical Model

The paper deals with shallow orthotropic shells of double curvature, square in plan, under dynamic loading. Outlines the ratios of the mathematical model of deformation considering the geometric nonlinearity, transverse shear and orthotropy material. For the formation of the ODE system is used method of Kantorovich. The resulting system is solved by the method of Rosenbrock. It is shown the verification of the proposed method for isotropic shells. For several options orthotropic shells made of fiberglass and carbon fiber studied their stability and obtained values of critical loads.

Analysis of Elastic Recovery Property Based on the Mesh Structure of Spun-Laced Nonwovens

2013 ◽  
Vol 659 ◽  
pp. 19-24
Author(s):  
Yin Jiang Zhang ◽  
Xiao Ping Xu ◽  
Xiang Yu Jin ◽  
Zhi Feng Zhang
Keyword(s):  
Elastic Recovery ◽  
Morphological Changes ◽  
Elastic Fiber ◽  
Static Friction ◽  
Mesh Structure ◽  
Static Friction Coefficient ◽  
Mesh Model ◽  
Longitudinal Extension ◽  
The Mathematical Model ◽  
Entanglement Structure

By means of entanglement and consolidation, fibers form stable web in spun-laced nonwovens, it initially conceived fibers entanglement structure and analyzed morphological changes in the stress state, the result showed that the elastic recovery property of spun-laced nonwovens could be adjusted through the deformation resilience of water mesh and the elastic fiber itself. Meanwhile the mathematical model demonstrated the most common "u-shaped" entanglement method between fibers,so fiber I slip from the fiber Π which met the equation T1 = T0×e μ θ. Under the same water jet pressure condition, larger static friction coefficient (μ) or fiber coated Angle (θ) equals better fiber entanglement, more stable structure and better elasticity. Combining the actual production with ideal mesh model, the size relations of horizontal and longitudinal extension deformation about Δ L and Δ L' was discussed. The results showed that the elastic recovery property of nonwovens could be improved through changing fibers arrangement of the fiber web.

scholarly journals Features of complex vibrations of flexible micropolar mesh panels

2021 ◽  
Vol 21 (1) ◽  
pp. 48-59
Author(s):  
Ekaterina Yu. Krylova ◽  
◽  
Irina V. Papkova ◽  
Olga A. Saltykova ◽  
Vadim A. Krysko ◽  
...  
Keyword(s):  
Initial Conditions ◽  
Equations Of Motion ◽  
Symmetric Tensor ◽  
Continuous Model ◽  
Cylindrical Panel ◽  
Particle Rotation ◽  
Differential Problem ◽  
Positive Direction ◽  
Mesh Structure ◽  
Hamilton Variational Principle

In this paper, a mathematical model of complex oscillations of a flexible micropolar cylindrical mesh structure is constructed. Equations are written in displacements. Geometric nonlinearity is taken into account according to the Theodore von Karman model. A non-classical continual model of a panel based on a Cosserat medium with constrained particle rotation (pseudocontinuum) is considered. It is assumed that the fields of displacements and rotations are not independent. An additional independent material parameter of length associated with a symmetric tensor by a rotation gradient is introduced into consideration. The equations of motion of a panel element, the boundary and initial conditions are obtained from the Ostrogradsky – Hamilton variational principle based on the Kirchhoff – Love’s kinematic hypotheses. It is assumed that the cylindrical panel consists of n families of edges of the same material, each of which is characterized by an inclination angle relative to the positive direction of the axis directed along the length of the panel and the distance between adjacent edges. The material is isotropic, elastic and obeys Hooke’s law. To homogenize the rib system over the panel surface, the G. I. Pshenichnov continuous model is used. The dissipative mechanical system is considered. The differential problem in partial derivatives is reduced to an ordinary differential problem with respect to spatial coordinates by the Bubnov – Galerkin method in higher approximations. The Cauchy problem is solved by the Runge – Kutta method of the 4th order of accuracy. Using the establishment method, a study of grid geometry influence and taking account of micropolar theory on the behavior of a grid plate consisting of two families of mutually perpendicular edges was conducted.

On the Buckling of a Two-Dimensional Micropolar Strip

2015 ◽  
Vol 82 (4) ◽  
Author(s):  
Armanj D. Hasanyan ◽  
Anthony M. Waas
Keyword(s):  
Geometric Nonlinearity ◽  
Linear Analysis ◽  
Buckling Analysis ◽  
Two Dimensional ◽  
Micropolar Theory ◽  
Classical Elasticity ◽  
Material Microstructure ◽  
Beam Equations ◽  
Limiting Case ◽  
Single Strip

This study examines the buckling of a single strip of material, modeled as a two-dimensional (2D) micropolar solid. The effects of material microstructure are incorporated by modeling the material using micropolar theory. By setting the micropolar constants to zero, the equations of classical elasticity are obtained and these results are compared to the buckling analysis performed by previous authors on elastic materials. In the limiting case, when the thickness of the strip becomes small in comparison to the overall length, the micropolar beam equations are developed. Because buckling analysis requires the consideration of geometric nonlinearity, nonlinear micropolar equations are derived using a variational procedure, which also results in variationally consistent boundary conditions. Due to the complexity of micropolar theory, its application has been limited to linear analysis with a few exceptions.

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