Abstract This paper presents an effective variational formalism of construction the thick anisotropic linear shell theory Vekua‐type arbitrary order. The dynamic equations are formulated as Lagrange second kind, independent from expansion functions. asymmetric stress tensor is used to obtain compact form similar classical theories. proposed approach allows one for computer‐aided derivation all using computer algebra software supporting main operations. Some solutions test problems presented.

A new approximate model of the tire rolling accounting for coupled longitudinal and lateral sliding as well spinning deformed state resulting in elastic forces is proposed. The main goal this investigation consists construction simple models with a few degrees freedom allowing one to implement them analytically engineering practice, primarily estimation stability prognosis instable so-called ”shimmy phenomenon” numerical simulation transient dynamics wheels effects. Such could become useful...

A new variant of the I. N. Vekua – A. Amosov extended theory thick anisotropic shells is constructed on groundwork Lagrange variational formalism analytical mechanics continua and dimensional reduction approach. The shell model consists in set field variables, surface Lagrangiandensity, constraint equations defined two-dimensional manifold corresponding to base surface. supplementary constraints are derived from boundary conditions shell's faces. variables first kind biorthogonal expansion's...

The dynamics of elastic functionally graded waveguides with symmetric through-thickness structure is considered on the background new formulation Nth-order plate theory. general model based Lagrangian formalism analytical and dimensional reduction approach combined biorthogonal expansion technique applied to spatial distribution displacement vector field. use compact basis shown, normal wave propagation in a plane waveguide modeled, convergence analyzed using isotropic homogeneous as test...

Предложена новая приближенная модель качения деформируемого колеса с пневматиком, позволяющая учесть как усилия в пневматике, так и влияние сил сухого трения на устойчивость прямолинейного при прогнозировании явления шимми. Модель основана теории комбинированнойкине матикойотно сительного движения соприкасающихся тел, т. е. одновременном качении, скольжении верчении учете реальнойф ормы области контакта распределения контактного давления. Главный вектор главный момент сил, возникающих...

An implementation of the theory multi-component dry friction in some engineering problems pneumatics’ dynamics is proposed. The main attention devoted to construction analytical models combined accounting for anisotropy coefficients and real distribution normal tangent contact stresses. These are applied more detailed investigation unsteady rolling regimes pneumatics which characterized by non-vanishing sliding spin.

The theory of multi-component dry friction accounting for the coupled kinematics relative motion in finite contact spots is applied to modelling pneumatic tires. analytical models combined anisotropy factors as well distribution pressure close real one are introduced. exact integral relationships between force and torque generalized velocities, i. e. speed sliding angular velocity spinning, appears a result integration over spot too complex be implemented analytically into engineering...

The numerical simulation of phase transitions in shape memory alloy beams under combined mechanical loads and temperature fields is performed on the background once coupled Movchan's theory thermoelastic transforms finite element approach. completely incremental formulation model behavior alloys constructed implemented into code. geometrically physically nonlinear solid used to investigate dynamics prismatic being axially compressed cooled through range direct martensite transforms. trivial...

О ВАРИАЦИОННЫХ УРАВНЕНИЯХ РАСШИРЕННОЙ ТЕОРИИ N-ГО ПОРЯДКА УПРУГИХ ОБОЛОЧЕК И ИХ ПРИЛОЖЕНИИ К НЕКОТОРЫМ ЗАДАЧАМ ДИНАМИКИ  О.В.Егорова 1 , С

The implementations of the theory multicomponent dry friction [1-19] for analyze dynamics some robotic systems, such as a butterfly robot [16-18, 20] or humanoid is proposed. Since main controlled element these systems spherical, elastic composite shell, it required to calculate distribution normal contact stresses inside spot. pressure elements constructed using S. A. Ambartsumyan’s equation transversally isotropic spherical shell. This modified by introducing averaged and displacements...

New incremental formulation of the compatibility equations for two-phase shape memory alloys is obtained on basis once coupled constitutive model, boundary value problem small increments stresses and phase volume ratio proposed, two stability concepts required to formulate linearized buckling problems are presented.

The plate theory of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math>th order is constructed on the background Lagrangian variational formalism analytical dynamics continuum systems and dimensional reduction approach I. N. Vekua – A. Amosov. model defined within configuration space, set field variables, density. variables are determined by coefficients biorthogonal expansion spatial displacement vector with respect to dimensionless normal coordinate....

Analysis of overhead power transmission lines (OPL) involves the simulation statics and oscillation. Solving such problems strictly requires proper accounting internal conductor structure, in particular for safety reliability systems information-telecommunication supply aerodromes aircraft systems, as well subjected to intense wind, especially icing conditions. Due complexity wire structures, known issues arise estimates their deformations, stiffness, bearing capacity, etc. For instance,...