Buckling of Elastic Composite Rods made of Micropolar Material Subjected to Combined Loads

Within the nonlinear Cosserat continuum, the stability of a compressed multilayer tube under internal and external hydrostatic pressures is studied. The tube is formed by attaching to each other N hollow cylinders that have been subjected to preliminary deformations of axial extension-compression and contains internal stresses. For the model of a physically linear micropolar material, the system of linearized equilibrium equations is derived, which describes the behavior of a multilayer cylindrical tube in a perturbed state. Using a special substitution, the stability analysis is reduced to solving a linear homogeneous boundary-value problem for a system of 6 N ordinary differential equations. In the case of a three-layer tube made of dense polyurethane foam, the stability regions were constructed in the planes of loading parameters (the relative axial compression and the relative external or internal pressure) for different preliminary deformations of inner and outer layers (coatings). According to the results obtained, the preliminary extension of both the outer and inner coatings generally stabilizes the considered deformations of the three-layer tube, while the effect of their preliminary compression is negative. It should be noted here that the pre-stressed outer coating has a more significant influence on the tube stability than the pre-stressed inner coating. In addition, the described effects of preliminary deformations are more pronounced for tubes with thicker coatings.

“…and the constitutive relations (2) for the Piola-type stress and couple stress tensors have the form [42,44]…”

Section: Governing Equations Of Micropolar Mediummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Influence of internal stresses on stability of multilayer micropolar tubes

Sheydakov

2022

“…The problem of equilibrium stability for deformable bodies is of major importance both from a theoretical and from a practical point of view [33]. The talk by Denis N Sheydakov (‘On stability of inhomogeneous elastic rod made of micropolar material’) was dedicated to the buckling analysis of nonlinearly elastic rods made of porous materials.…”

Section: Thematic Sessionsmentioning

confidence: 99%

Euromech 563 Cisterna di Latina 17–21 March 2014 Generalized continua and their applications to the design of composites and metamaterials: A review of presentations and discussions

Placidi

Giorgio

Corte

et al. 2016

In the present paper, a rational report on Euromech 563, Generalized continua and their applications to the design of composites and metamaterials (Cisterna di Latina 17–21 March 2014), is provided. The frank and constructive spirit which animated the workshop by Dell’Isola et al. ( ZAMM 2014; 94(5): 367–372) also characterized Euromech Colloquium 563. All presentations were video-recorded and are freely available online at the address http://www.memocsevents.eu/euromech563/?page_id=1013 . The topics treated were selected by the organizers in order to allow a comparison of the available experimental evidence with the predictive capability of current theoretical models. The numerical investigations selected and presented aimed to make more effective the aforementioned comparison. The interested reader will find more details about the colloquium at the dedicated webpage http://www.memocsevents.eu/euromech563 . The design and use of advanced materials and structural elements requires an extensive and rigorous process of mathematical modeling. The organizers of Euromech 563, being aware of this need, have chosen as participants renowned and reputed scientists (and some promising young researchers) who all agree on recognizing to mathematical sciences their role of unifying and coordinating tool in the effort for the advance of technology. The Colloquium has indeed surely contributed to the development of more advanced technological possibilities and to the theoretical conception of completely new ones.

“…Representations of the linearized Piola-type stress tensor D • and couple stress tensor G • for physically linear material (8) are obtained by linearization of the constitutive equations (2) with regard to the relations (13) [33]:…”

Section: The Equations Of Neutral Equilibriummentioning

confidence: 99%

“…According to the relations (5)–(7), (9), (13), (15)–(17), the components of the linearized Piola-type stress tensor D • and couple stress tensor G • are given by the following formulas [33]:…”

Section: The Equations Of Neutral Equilibriummentioning

confidence: 99%

Stability of inhomogeneous micropolar cylindrical tube subject to combined loads

Sheydakov

Altenbach

2016

In the present paper, the stability of a nonlinear elastic cylindrical tube made of micropolar material is analyzed. It is assumed that the elastic properties of the tube vary through the wall thickness. The problem is studied for the case of axial compression of the tube under internal and external hydrostatic pressure. Applying linearization the neutral equilibrium equations have been derived, which describe the perturbed state of the tube. By solving these equations numerically the critical curves and corresponding buckling modes have been found, and the stability regions have been constructed in the planes of loading parameters (relative axial compression, relative internal or external pressure). Using these results, the influence of elastic properties, as well as the size of the tube, on the loss of stability is studied. Special attention has been paid to the analysis of how the pattern of change in elastic parameters affects the stability of a cylindrical tube made of micropolar material.