On minimum-principles for the initial-boundary-value problem of elastic-plastic plates with moderate rotations

1983 ◽  
Vol 53 (1) ◽  
pp. 13-25 ◽  
Author(s):  
D. Weichert
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Elastic Plastic ◽  
Initial Boundary Value

scholarly journals REFINED MODEL OF VISCO-ELASTIC-PLASTIC DEFORMATION OF REINFORCED FLEXIBLE SHALLOW SHELLS

2019 ◽  
Vol 81 (4) ◽  
pp. 461-473
Author(s):  
A.P. Yankovskii
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Plastic Behavior ◽  
Face Surface ◽  
Shallow Shells ◽  
Elastic Plastic ◽  
Initial Boundary Value

The initial-boundary value problem of the visco-elastic-plastic behavior of flexible shallow shells reinforced along parallel surfaces is formulated. The inelastic behavior of the materials of the components of the composition is described by the equations of the theory of plastic flow with isotropic hardening. Viscoelastic deformation is determined by the relations of the Maxwell -Boltzmann model. Geometric nonlinearity is taken into account in the Karman approximation. The obtained resolving equations and boundary conditions allow with varying degrees of accuracy to determine the stress-strain state (including the residual state) in the components of the composition of curved panels. The low resistance of the reinforced structure to transverse shear is taken into account. In the first approximation, the equations and boundary conditions corresponding to the traditional non-classical Reddy theory follow from the relations obtained. The numerical solution of the formulated initial-boundary value problem is based on an explicit “cross” scheme. The features of visco-elastic-plastic dynamic deformation of an orthogonal reinforced cylindrical rectangular panel under the action of a load caused by an air blast wave are investigated. It is shown that in some cases even for relatively thin reinforced shallow shells, Reddy's theory is unacceptable for obtaining adequate results of calculations of their visco-elastic-plastic dynamic behavior. It has been demonstrated that the shape and size of the residual deflections of curved composite panels substantially depend on which face surface of the structure (convex or concave) an external load is applied. It was found that in both cases of loading, residual deflections lead to the formation of longitudinal folds in a thin cylindrical reinforced panel.

scholarly journals REFINED MODEL OF VISCO-ELASTIC-PLASTIC DEFORMATION OF REINFORCED FLEXIBLE SHALLOW SHELLS

2019 ◽  
Vol 81 (4) ◽  
pp. 462-474
Author(s):  
A.P. Yankovskii
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Plastic Behavior ◽  
Face Surface ◽  
Shallow Shells ◽  
Elastic Plastic ◽  
Initial Boundary Value

The initial-boundary value problem of the visco-elastic-plastic behavior of flexible shallow shells reinforced along parallel surfaces is formulated. The inelastic behavior of the materials of the components of the composition is described by the equations of the theory of plastic flow with isotropic hardening. Viscoelastic deformation is determined by the relations of the Maxwell -Boltzmann model. Geometric nonlinearity is taken into account in the Karman approximation. The obtained resolving equations and boundary conditions allow with varying degrees of accuracy to determine the stress-strain state (including the residual state) in the components of the composition of curved panels. The low resistance of the reinforced structure to transverse shear is taken into account. In the first approximation, the equations and boundary conditions corresponding to the traditional non-classical Reddy theory follow from the relations obtained. The numerical solution of the formulated initial-boundary value problem is based on an explicit “cross” scheme. The features of visco-elastic-plastic dynamic deformation of an orthogonal reinforced cylindrical rectangular panel under the action of a load caused by an air blast wave are investigated. It is shown that in some cases even for relatively thin reinforced shallow shells, Reddy's theory is unacceptable for obtaining adequate results of calculations of their visco-elastic-plastic dynamic behavior. It has been demonstrated that the shape and size of the residual deflections of curved composite panels substantially depend on which face surface of the structure (convex or concave) an external load is applied. It was found that in both cases of loading, residual deflections lead to the formation of longitudinal folds in a thin cylindrical reinforced panel.

RESEARCH OF THE IMPACT DEVICE MODEL OF THE ROD TYPE BY DIFFERENCE METHOD

2020 ◽  
pp. 73-80
Author(s):  
А.М. Слиденко ◽  
В.М. Слиденко
Keyword(s):  
Boundary Value Problem ◽  
Difference Method ◽  
Model Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Cross Sectional ◽  
Impact Device ◽  
Initial Boundary Value ◽  
The Impact

Приводится анализ механических колебаний элементов ударного устройства с помощью модели стержневого типа. Ударник и инструмент связаны упругими и диссипативными элементами, которые имитируют их взаимодействие. Аналогично моделируется взаимодействие инструмента с рабочей средой. Сформулирована начально-краевая задача для системы двух волновых уравнений с учетом переменных поперечных сечений стержней. Площади поперечных сечений определяются параметрическими формулами при сохранении объемов стержней. Параметрические формулы позволяют получать различного вида зависимости площади поперечного сечения стержня от его длины. Начальные условия отражают физическую картину взаимодействия инструмента с ударником и рабочей средой. Краевые условия описывают контактные взаимодействия ударника с инструментом и последнего с рабочей средой. В качестве модельной задачи рассматривается соударение ударника и инструмента через элемент большой жесткости. Начально-краевая задача исследуется разностным методом. Проводится сравнение решений задачи, полученных с помощью двухслойной и трехслойной разностных схем. Такие схемы реализованы в общей компьютерной программе в системе Mathcad. Показано, что при вычислениях распределения нормальных напряжений по длине стержня лучшими свойствами относительно устойчивости обладает двухслойная схема The article gives the analysis of mechanical vibrations of the impact device elements using the model of the rod type. The hammer and the tool are connected by elastic and dissipative elements that simulate their interaction. The interaction of the tool with the processing medium is simulated in a similar way. An initial boundary-value problem is formulated for a system of two wave equations taking into account the variable cross sections of the rods. Cross-sectional areas are determined by parametric formulas maintaining the volume of the rods. Parametric formulas allow one to obtain various dependence types of the cross-sectional area of the rod on its length. The initial and boundary conditions reflect the physical phenomenon of the tool interaction with the processing medium, and also describe the contact interactions of the hammer with the tool. The impacting of the hammer and the tool through an element of high rigidity is considered as a model problem. To control the limiting values, the solution of the model problem by the Fourier method is used. The initial-boundary-value problem is investigated by the difference method. A comparison of solutions obtained for the two-layer and three-layer difference schemes is given. Such schemes are realized in a common computer program in the Mathcad. It is shown that the two-layer scheme has the best properties in relation to stability while calculating the distribution of normal voltage along the length of the rod

scholarly journals Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Liming Xiao ◽  
Mingkun Li
Keyword(s):  
Weak Solution ◽  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Higher Order ◽  
Evolution Problem ◽  
Positive Energy ◽  
Initial Boundary Value

AbstractIn this paper, we study the initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations which do not have positive energy and come from the soil mechanics, the heat conduction, and the nonlinear optics. By the mountain pass theorem we first prove the existence of nonzero weak solution to the static problem, which is the important basis of evolution problem, then based on the method of potential well we prove the existence of global weak solution to the evolution problem.

scholarly journals An extension of Gronwall inequality in the theory of bodies with voids

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1161-1167
Author(s):  
Marin Marin ◽  
Praveen Ailawalia ◽  
Ioan Tuns
Keyword(s):  
Boundary Value Problem ◽  
Internal State ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Uniqueness Result ◽  
Internal Variables ◽  
State Variables ◽  
Gronwall’S Inequality ◽  
Initial Boundary Value

Abstract In this paper, we obtain a generalization of the Gronwall’s inequality to cover the study of porous elastic media considering their internal state variables. Based on some estimations obtained in three auxiliary results, we use this form of the Gronwall’s inequality to prove the uniqueness of solution for the mixed initial-boundary value problem considered in this context. Thus, we can conclude that even if we take into account the internal variables, this fact does not affect the uniqueness result regarding the solution of the mixed initial-boundary value problem in this context.

Sign in / Sign up

Export Citation Format

Share Document