Ray Series Method for the Analysis of Dynamic Problems of Contact Interaction

The problem on low-velocity impact of an elastic body upon a pre-stressed circular orthotropic plate possessing cylindrical anisotropy is considered. The dynamic behavior of the plate is described by equations taking the rotary inertia and transverse shear deformations into account. Longitudinal compressing forces are uniformly distributed along the plate’s median plane. Contact interaction is modeled by a linear spring, and a force arising in it is the linear approximation of Herts’z contact force. During the shock interaction of the impactor with the plate, the waves which are the surfaces of strong discontinuity are generated in the plate and begin to propagate. Behind the fronts of these waves, the solution is constructed in terms of ray series, which coefficients are the different order discontinuities in partial time-derivatives of the desired functions, and a variable is the time elapsed after the wave arrival at the plate’s point under consideration. The ray series coefficients are determined from recurrent equations within accuracy of arbitrary constants, which are then determined from the conditions of dynamic contact interaction of the impactor with the target. The found arbitrary constants allow one to construct the solution both within and out of the contact region. The analysis of the solution obtained enables one to find out the new effect and to make the inference that under a certain critical magnitude of the compression force the orthotropic plate goes over into the critical state, what is characterized by ‘locking’ the shear wave within the contact region, resulting in plate damage within this zone as soon as the compression force exceeds its critical value.

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Noncompressed cylindrical layer shock loading in anisothermic conditions

Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния ◽

10.37972/chgpu.2020.16.30.026 ◽

2020 ◽

pp. 229-237

Author(s):

Виктор Игоревич Штука

Keyword(s):

Numerical Calculation ◽

Shock Loading ◽

Cylindrical Layer ◽

Series Method ◽

Incompressible Medium ◽

Strong Discontinuities ◽

Elastoplastic Deformations ◽

Polarized Waves ◽

Unsteady Effect ◽

Ray Series

На примере нескольких задач о нагружении упруговязкопластического и термоупругого цилиндрических слоёв с предварительными деформациями показаны основные моменты, на которые следует обратить внимание при комплексном моделировании отклика на существенно нестационарное воздействие термоупругой несжимаемой среды с вязкопластическими свойствами. Отмечены нюансы, касающиеся употребления соотношений теории больших упругопластических деформаций, применения метода лучевых рядов и использования специальных схем численных расчётов. Представлены зависимости скачков температуры и добавочного давления на плоскополяризованных поверхностях сильного разрыва, определены скорости волн нагрузки и круговой поляризации. The main points witch should be paid attention of modeling the response of thermoelastic incompressible medium with viscoplastic properties to the essentially unsteady effect are shown by the example of several problems on loading elastoviscoplastic and thermoelastic cylindrical layers with preliminary deformations. Some remarks were noted regarding to the use of the relations of the theory of finite elastoplastic deformations, the ray series method application and special numerical calculation schemes. The dependencies of temperature and additional pressure breaks on plane-polarized strong discontinuities surfaces, loading and circular polarized waves velocities are determined.

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Effect of Contact Interaction on the Stress Intensity Factors for a Crack under Harmonic Loading

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.5-6.173 ◽

2006 ◽

Vol 5-6 ◽

pp. 173-180 ◽

Cited By ~ 1

Author(s):

O.V. Menshykov ◽

I.A. Guz

Keyword(s):

Contact Interaction ◽

Boundary Integral Equations ◽

Boundary Integral ◽

Harmonic Loading ◽

Dynamic Problems ◽

Intensity Factors ◽

Penny Shaped Crack ◽

Shaped Crack ◽

Cracked Solids ◽

Crack Faces

This paper concerns fracture dynamic problems for elastic cracked solids with allowance for crack faces contact interaction. The contact problem for a penny-shaped crack with an initial opening under normally incident tension-compression wave is solved by the method of boundary integral equations. The solution is compared with those obtained without allowance for crack faces contact interaction for various values of the initial opening.

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Three-Dimensional Reconstruction of Two Forms of the Chaperonin GRO EL

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100180045 ◽

1990 ◽

Vol 48 (1) ◽

pp. 258-259

Author(s):

J.L. Carrascosa ◽

G. Abella ◽

S. Marco ◽

M. Muyal ◽

J.M. Carazo

Keyword(s):

Three Dimensional ◽

The Other ◽

Two Dimensional ◽

Series Method ◽

Three Dimensional Reconstruction ◽

Structural Components ◽

E Coli ◽

Dimensional Reconstruction ◽

Morphogenetic Factors ◽

Tilt Series

Chaperonins are a class of proteins characterized by their role as morphogenetic factors. They trantsiently interact with the structural components of certain biological aggregates (viruses, enzymes etc), promoting their correct folding, assembly and, eventually transport. The groEL factor from E. coli is a conspicuous member of the chaperonins, as it promotes the assembly and morphogenesis of bacterial oligomers and/viral structures.We have studied groEL-like factors from two different bacteria:E. coli and B.subtilis. These factors share common morphological features , showing two different views: one is 6-fold, while the other shows 7 morphological units. There is also a correlation between the presence of a dominant 6-fold view and the fact of both bacteria been grown at low temperature (32°C), while the 7-fold is the main view at higher temperatures (42°C). As the two-dimensional projections of groEL were difficult to interprete, we studied their three-dimensional reconstruction by the random conical tilt series method from negatively stained particles.

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