Showing papers in "Archive of Applied Mechanics in 2022"

Revisiting the dynamics of finite-sized satellite near the planet in ER3BP

Abstract: A novel approach for solving equations of motion of finite-sized satellite supposed to be moving in a proximity and around the planet in the elliptic restricted three-body problem, ER3BP is presented in this semi-analytical investigation. We consider two primaries, M_Sun and m_planet (the last is secondary in that binary system), both are orbiting around their barycenter on elliptic orbits. Satellite is considered to be the solid ellipsoid having nearly spherical form, with its gravitational potential to be given by a formula of MacCullagh type. Our aim is to revisit previously presented in work [Ashenberg, 1996] approach and to investigate the updated type of the satellite dynamics correlated implicitly to a kind of trapped motion (in the synodic co-rotating Cartesian coordinate system) in so way that satellite will always to be located near the secondary planet, m_planet, moving on quasi-stable elliptic orbit.

Seventy years of tensegrities (and counting)

Abstract: Abstract We try to make a long way short by proceeding per exempla from Kenneth Snelson’s sculptures and Richard Buckminster Fuller’s coinage of the term tensegrity to modern tensegrity metamaterials. We document the passage from initial interest in tensegrity frameworks for their visual impact to today’s interest, driven by their peculiar structural performances. In the past seventy years, the early art pieces and roofing structural complexes have been followed by formalization of the principles governing the form-finding property of ‘pure’ tensegrity structures and by engineering hybridization leading to a host of diverse practical applications, such as variable-geometry civil engineering structures, on-earth and in-orbit deployable structures and robots, and finally to recent and promising studies on tensegrity metamaterials and small-scale tensegrity structures.

Nonlinear suppression using time-delayed controller to excited Van der Pol–Duffing oscillator: analytical solution techniques

Abstract: Abstract To suppress the nonlinearity of an excited Van der Pol–Duffing oscillator (VdPD), time-delayed position and velocity are used throughout this study. The time delay is supplemental to prevent the nonlinear vibration of the considered system. The topic of this work is extremely current because technologies with a time delay have been the subject of several studies in the latest days. The classical homotopy perturbation method (HPM) is utilized to extract an approximate systematic explanation for the system at hand. Furthermore, a modification of the HPM reveals a more accurate approximate solution. This accuracy is tested through a comparison with the numerical solution. The practical approximate analytical methodology makes the work possible to qualitatively evaluate the results. The time histories of the obtained solutions are drawn for various values of the natural frequency and the time delay parameters. Discussion of the results is presented in light of the plotted curves. On the other hand, the multiple scale procedure examines the organized nonlinear prototypical approach. The influence of the diverse regulatory restrictions on the organization’s vibration performances is explored. Two important cases of resonance, the sub-harmonic and super-harmonic, are examined according to the cubic nonlinearity. The modulation equations achieved for these cases are examined graphically according to the impact of the used parameters.

Mechanical characterization of composite materials with rectangular microstructure and voids

Abstract: Abstract The purpose of this work is to study the mechanical behavior of microstructured materials, in particular porous media. We consider a detailed description of the material through a discrete model, considered as the benchmark of the problem. Two continuous models, one micropolar and one classic, obtained through a homogenization procedure of the material, are studied both in static and dynamic conditions. Furthermore, the internal characteristics of the material, such as the internal scale of the microstructure and the percentage of the voids, are made to vary in order to investigate the mechanical response and to have an exhaustive comparison among the models.

On dynamic modeling of piezomagnetic/flexomagnetic microstructures based on Lord–Shulman thermoelastic model

Abstract: Abstract We study a time-dependent thermoelastic coupling within free vibrations of piezomagnetic (PM) microbeams considering the flexomagnetic (FM) phenomenon. The flexomagneticity relates to a magnetic field with a gradient of strains. Here, we use the generalized thermoelasticity theory of Lord–Shulman to analyze the interaction between elastic deformation and thermal conductivity. The uniform magnetic field is permeated in line with the transverse axis. Using the strain gradient approach, the beam yields microstructural properties. The analytical solving process has been gotten via applying sine Fourier technique on displacements. Graphical illustrations are assigned to shape numerical examples concerning variations in essential physical quantities. It was observed that the flexomagnetic effect could be extraordinary if the thermal conductivity of the material is higher or the thermal relaxation time of the heat source is lesser. This theoretical study will provide the way of starting studies on magneto-thermoelastic small-scale piezo-flexomagnetic structures based on the heat conduction models.

Simulation of crack propagation based on eigenerosion in brittle and ductile materials subject to finite strains

Abstract: Abstract In this paper, a framework for the simulation of crack propagation in brittle and ductile materials is proposed. The framework is derived by extending the eigenerosion approach of Pandolfi and Ortiz (Int J Numer Methods Eng 92(8):694–714, 2012. 10.1002/nme.4352 ) to finite strains and by connecting it with a generalized energy-based, Griffith-type failure criterion for ductile fracture. To model the elasto-plastic response, a classical finite strain formulation is extended by viscous regularization to account for the shear band localization prior to fracture. The compression–tension asymmetry, which becomes particularly important during crack propagation under cyclic loading, is incorporated by splitting the strain energy density into a tensile and compression part. In a comparative study based on benchmark problems, it is shown that the unified approach is indeed able to represent brittle and ductile fracture at finite strains and to ensure converging, mesh-independent solutions. Furthermore, the proposed approach is analyzed for cyclic loading, and it is shown that classical Wöhler curves can be represented.

Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters

Abstract: Abstract Optimized material parameters obtained from parameter identification for verification wrt a certain loading scenario are amenable to two deficiencies: Firstly, they may lack a general validity for different loading scenarios. Secondly, they may be prone to instability, such that a small perturbation of experimental data may ensue a large perturbation for the material parameters. This paper presents a framework for extension of hyperelastic models for rubber-like materials accounting for both deficiencies. To this end, an additive decomposition of the strain energy function is assumed into a sum of weighted strain mode related quantities. We propose a practical guide for model development accounting for the criteria of verification, validation and stability by means of the strain mode-dependent weighting functions and techniques of model reduction. The approach is successfully applied for 13 hyperelastic models with regard to the classical experimental data on vulcanized rubber published by Treloar (Trans Faraday Soc 40:59–70, 1944), showing both excellent fitting capabilties and stable material parameters.

Moderately large deflection of slightly curved layered beams with interlayer slip

Abstract: Abstract This paper presents a beam theory for analyzing the static response of slightly curved three-layer beams with interlayer slip. Since the beams are supposed to be immovably supported, membrane stresses develop even at moderately large deflections and the response becomes geometrically nonlinear. The theory is based on a layerwise application of the Euler–Bernoulli theory and a linear elastic constitutive law for the interlaminar displacements. In three application examples, the accuracy of this theory is shown by comparing the results of this theory with the outcomes of a more complex finite element analysis assuming a plane stress state. These application examples demonstrate the effect of a small initial deflection on the nonlinear response of the considered layered structural members.