ISSN:
eISSN:
1450-5584
2406-0925

Theoretical and Applied Mechanics

Теоријска и примењена механика

Articles in Press


Ut Vis Sic Tensio
Giuseppe Saccomandi
Available online 03 November 2017

Abstract
The mechanical properties of rubber-like materials have been offering an outstanding challenge to the solid mechanics community for a long time. The behaviour of such materials is quite difficult to predict because rubber self-organizes into mesoscopic physical structures that play a prominent role in determining their complex, history-dependent and strongly nonlinear response. In this framework one of the main problems is to find a functional form of the elastic strain-energy that best describes the experimental data in a mathematical feasible way. The aim of this paper is to give a survey of recent advances aimed at solving such a problem.

Mathematics Subject Classification
74B20

Keywords
hyper-elasticity, simple extension, phenomenological reduction, non-Gaussian effects

DOI
https://doi.org/10.2298/TAM170703011S


Variational model of scoliosis
Igor Popov, Nikita Lisitsa, Yuri Baloshin, Mikhail Dudin, and Stepan Bober
Available online 07 November 2017

Abstract
Scoliosis, being one of the most widespread spine diseases among children, has been studied extensively throughout the history of medicine, yet there is no clear understanding of its initiating factors and the mechanogenesis of the monomorphic three-dimensional deformation due to its polyetiological nature. We present a novel mathematical model of the process of emergence of three-dimensional deformation of human spine based on variational principles. Typical scoliosis geometry is assumed to be described as minimal curves of a particular energy functional, which are shown to closely resemble actual scoliosis. The numerical properties of the first stage of scoliosis are investigated, which is shown to have the highest influence on the development of the disease.

Mathematics Subject Classification
92C10; 74L15

Keywords
spine, model, variational method

DOI
https://doi.org/10.2298/TAM170818012P


Locomotion of multibody robotic systems: dynamics and optimization
Felix L. Chernousko
Available online 09 February 2018

Abstract
Locomotion of multibody systems in resistive media can be based on periodic change of the system configuration. The following types of mobile robotic systems are examined in the paper: multilink snake-like systems; multibody systems in quasi-static motion; systems consisting of several interacting bodies; fish-like, frog-like, and boat-like systems swimming in fluids; systems containing moving internal masses. Dynamics of these systems subjected to various resistance forces, both isotropic and anisotropic, are investigated, including dry friction forces obeying Coulomb\mbox{'}s law and forces directed against the velocity of the moving body and proportional to the velocity value or its square. Possible modes of locomotion and control algorithms are discussed. Optimization for various types of mobile robots is considered. Optimal values of geometrical and mechanical parameters as well as optimal controls are obtained that provide the maximum locomotion speed or minimum energy consumption. Results of experiments and computer simulation are discussed.

Mathematics Subject Classification
70E55

Keywords
multibody systems, robotics, locomotion, optimization

DOI
https://doi.org/10.2298/TAM171017001C