Comparative assessments of strain measures for nonlinear analysis of truss structures at large deformations

PurposeIn this paper the use of classical strain measures in analysis of trusses at finite deformations will be discussed. The results will be compared to the ones acquired using a novel strain measure based on the Hyperbolic Sine function. Through the evaluation of results, algebraic development and graph analysis, the properties of the Hyperbolic Sine strain measure will be examined.Design/methodology/approachThrough graph plotting, comparisons between the novel strain measure and the classic ones will be made. The formulae for the implementation of the Hyperbolic Sine strain measure into a positional finite element method are developed. Four engineering applications are presented and comparisons between results obtained using all strain measures studied are made.FindingsThe proposed strain measure, Hyperbolic Sine, has objectivity and symmetry. The linear constitutive model formed by the Hyperbolic Sine strain and its conjugated stress presents an increasing stiffness, both in compression and tension, a behavior that can be useful in the modeling of several materials.Research limitations/implicationsThe structural analysis performed on the four examples of trusses in this article did not consider the variation of the cross-sectional area of the elements or the buckling phenomenon, moreover, only elastic behavior is considered.Originality/valueThe present article proposes the use of a novel strain measure family, based on the Hyperbolic Sine function and suitable for structural applications. Mathematical expressions for the use of the Hyperbolic Sine strain measure are established following the energetic concepts of the positional formulation of the finite element method.

Robust adaptive filtering algorithms based on (inverse)hyperbolic sine function

Recently, adaptive filtering algorithms were designed using hyperbolic functions, such as hyperbolic cosine and tangent function. However, most of those algorithms have few parameters that need to be set, and the adaptive estimation accuracy and convergence performance can be improved further. More importantly, the hyperbolic sine function has not been discussed. In this paper, a family of adaptive filtering algorithms is proposed using hyperbolic sine function (HSF) and inverse hyperbolic sine function (IHSF) function. Specifically, development of a robust adaptive filtering algorithm based on HSF, and extend the HSF algorithm to another novel adaptive filtering algorithm based on IHSF; then continue to analyze the computational complexity for HSF and IHSF; finally, validation of the analyses and superiority of the proposed algorithm via simulations. The HSF and IHSF algorithms can attain superior steady-state performance and stronger robustness in impulsive interference than several existing algorithms for different system identification scenarios, under Gaussian noise and impulsive interference, demonstrate the superior performance achieved by HSF and IHSF over existing adaptive filtering algorithms with different hyperbolic functions.

Analysis, Synchronization, and Robotic Application of a Modified Hyperjerk Chaotic System

In this work, a novel hyperjerk system, with hyperbolic sine function as the only nonlinear term, is proposed, as a modification of a hyperjerk system proposed by Leutcho et al. First, a dynamical analysis on the system is performed and interesting phenomena concerning chaos theory, such as route to chaos, antimonotonicity, crisis, and coexisting attractors, are studied. For this reason, the system’s bifurcation diagrams with respect to different parameter values are plotted and its Lyapunov exponents are computed. Afterwards, the synchronization of the system is considered, using active control. The proposed system is then applied, as a chaotic generator, to the problem of chaotic path planning, using a combination of sampling and a modulo tactic technique.

Hot workability of V-Ti microalloyed steel for forging

The hot compression and the hot tensile experiments were carried out on a Gleeble3800 thermal-mechanical simulator at different deformation conditions. The relationship between the flow stress and Zener-Hollomon parameter was established by the hyperbolic sine function. The hot deformation apparent activation energy is about 371 kJ/mol. There are two peak regions of m-value in the m maps with true strain of 0.2. One peak corresponds to the temperature of 1050 °C and the strain rate of 0.01 s−1, the other one corresponds to the temperature of 1200 °C and the strain rates within range of 0.1 s−1 ∼ 1 s−1. There is only one peak region (1150 °C ∼ 1200 °C, 0.1 s−1 ∼ 1 s−1) of m-value, when true strain is 0.4 or 0.9. The reduction of area increases from 65% to 98% with the temperature increases from 800 °C to 1200 °C. In temperature range of 1000 °C ∼ 1200 °C, the reduction of area is always over 90%, which means that the plasticity of the steel is fine. According to the results of the research, it can be proved that the optimal deformation conditions with different strain correspond to the peak regions of m-value. The optimum deformation conditions is the temperature of 1200 °C and the strain rates within range of 0.1 s−1 ∼ 1 s−1, which were suitable for the true strain with 0.2, 0.4 and 0.9 at the same time.

A Novel Autonomous 5-D Hyperjerk RC Circuit with Hyperbolic Sine Function

A novel autonomous 5-D hyperjerk RC circuit with hyperbolic sine function is proposed in this paper. Compared to some existing 5-D systems like the 5-D Sprott B system, the 5-D Lorentz, and the Lorentz-like systems, the new system is the simplest 5-D system with complex dynamics reported to date. Its simplicity mainly relies on its nonlinear part which is synthetized using only two semiconductor diodes. The system displays only one equilibrium point and can exhibit both periodic and chaotic dynamical behavior. The complex dynamics of the system is investigated by means of bifurcation analysis. In particular, the striking phenomenon of multistability is revealed showing up to seven coexisting attractors in phase space depending solely on the system’s initial state. To the best of author’s knowledge, this rich dynamics has not yet been revealed in any 5-D dynamical system in general or particularly in any hyperjerk system. Pspice circuit simulations are performed to verify theoretical/numerical analysis.