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The landing gear plays a very important role during landing by absorbing the high impact energy of the aircraft. The main landing gear absorbs the bulk of the load to reduce the load experienced by both the aircraft fuselage and the nose landing gear. In this paper, a mathematical approach is used to extract the dynamic characteristics of the system. A two-degree of freedom mathematical model of the main landing gear is developed. This model is used to derive the dynamic equations of the landing gear system and to study the behaviour of main landing gear during main gear and nose gear touchdown conditions. The non-linear stiffness and damping co-efficient in an Oleo-Pneumatic shock absorber are integrated into the system to achieve a more accurate response of the system. The response of this system is established by adopting a complex modal analysis approach to account for the non-classical damping exhibited by the system. The obtained spring force, damping force and responses are reported. This work provides an alternative approach using complex modal analysis to obtain results for complex systems exhibiting non-linear characteristics. [ABSTRACT FROM AUTHOR]

The Floquet theory that is used in order to find the stop-bands is not defined for non-linear cases. The eigenfrequencies of a symmetrical periodicity cell can serve as alternative indicators of stop-band boundaries. In the linear cases, eigenfrequencies of a structure with symmetrical boundary conditions are exactly placed on stop-bands boundaries. In the non-linear cases, however, the notion of the Floquet zones are not clearly defined. However, the eigenfrequencies method show the stop-band positions that agree with the energy flow analysis. In the cases are considered, the axial rod vibration, the radial-periodic membrane case, the axial rods connected with spring with non-linear stiffness. [ABSTRACT FROM AUTHOR]

Highlights • A theoretical method is proposed to design a compliant mechanism whose stiffness matches a predefined non-linear stiffness profile, which is "small loads, low stiffness and large loads, high stiffness", a common scenario widely existing in physical world. • The genetic algorithm was used to optimize the dimensions of proposed compliant mechanism. • The simulation about three different radius rollers and three formats of non-linear stiffness profiles was done, and good results prove the proposed method effective. • The experimental results show high accuracy of stiffness profiles of the prototype of a compliant actuator compared to the given non-linear stiffness profile. Abstract Compliant actuators are able to perform the safe interaction between robotics and human or unstructured environment owing to their intrinsic compliant attribute. A compliant actuator with constant stiffness is easy to be designed but has some limitations in bandwidth. Compliant actuators with variable stiffness get better ability of environment adaption, but their mechanisms are almost complex and bulky. This paper proposed a new design methodology of compliant mechanisms whose stiffness matches the predefined a non-linear stiffness profile "small loads, low stiffness and large loads, high stiffness", which is a common scenario of interaction in physical world. Owing to this idea, a compact compliant mechanism with predefined non-linear stiffness profile is proposed where a cantilever is used as basic elastic element with a special curve profile contacting with a roller. The new proposed actuator was adopted in compliant joints of rehabilitation robotic developed by ourselves. Meanwhile, three kinds of deflection-torque curves were implemented in simulation. At last, experimental and simulation results proved that the proposed method was effective to design the compliant mechanism to fulfill the predefined deflection-torque relationship of compliant non-linear stiffness actuators. [ABSTRACT FROM AUTHOR]

[Display omitted] • Mechanical metamaterials showing tunable non-linear strain-stiffening • Strain-stiffening by deformation-induced transitions in nodal topology • Fundamental principle independent of loading conditions • Tunable mechanical response by unit cell geometry and combination of unit cells Mechanical metamaterials are periodic lattice structures with complex unit cell architectures that can achieve extraordinary mechanical properties beyond the capability of bulk materials. A class of metamaterials is proposed, whose mechanical properties rely on deformation-induced transitions in nodal-topology by formation of internal self-contact. The universal nature of the principle presented, is demonstrated for tension, compression, shear and torsion. In particular, it is shown that by frustration of soft deformation modes, large highly non-linear stiffening effects can be generated. The tunable non-linear modulus increase can be exploited to design materials mimicking the complex mechanical response of biological tissue. [ABSTRACT FROM AUTHOR]

This contribution considers the nonlinearity of stiffness in granular materials using 3D DEM simulations, with a primary focus being placed on three issues. First, it assesses stress-dependent stiffness and density-dependent stiffness based on DEM simulations of monotonic triaxial tests. The modified formulation of hyperbolic relation based on the DEM data is generated to capture stiffness degradation, which can take the various types of an S-shaped curve due to the initial mean effective stress and the sample density. The use of various void ratio correction functions is made to remove the effect of density on the stiffness curve. DEM results reveal that inclusion of the coordination number in both forms of the void ratio function serve a better role in unifying the stiffness dataset from samples with different densities. Second, the framework of kinematic modified yielding points proposed by Jardine (1992) that identifies three main zones (i.e. linear elastic behaviour, non-linear elastic behaviour and elasto-plastic behaviour) provides a benchmark for the gap between the dynamic stiffness and the static stiffness to be studied in an effective manner. A key observation is that the dynamic shear stiffness tends to increase to a peak value before experiencing of a decrease in magnitude. Third, the investigation into the nature of energy dissipation during triaxial shearing tests is made. Several DEM simulations were performed to assess effects of the coefficient of uniformity (C u) on the non-linear behaviour of granular materials, arriving at some key observations that: (i) a higher amount of work should be input for samples with coarse particles to attain a particular strain level; and (ii) more energy dissipation is observed for samples with a lower C u value. [Display omitted] • The modified formulation of hyperbolic relation based on the DEM data is generated to capture stiffness degradation, which can take the various types of an S-shaped curve due to the initial mean effective stress and the sample density. • DEM results reveal that inclusion of the coordination number in both forms of the void ratio function serve a better role in the removal of void ratio effects on the stiffness degradation curve. • Several DEM simulations were performed to assess effects of the coefficient of uniformity (C u) on the non-linear behaviour of granular materials, arriving at some key observations that: (i) a higher amount of work should be input for samples with coarse particles to attain a particular strain level; and (ii) more energy dissipation is observed for samples with a lower C u value. • The framework of kinematic modified yielding points proposed by Jardine (1992) that identifies three main zones (i.e. linear elastic behaviour, non-linear elastic behaviour and elasto-plastic behaviour) provides a benchmark for the gap between the dynamic stiffness and the static stiffness to be studied in an effective manner. • A key observation is that the dynamic shear stiffness tends to increase to a peak value before experiencing of a decrease in magnitude. [ABSTRACT FROM AUTHOR]

The article discusses a study which compares centrifuge and numerical models of the slope failure of foliated rock mass obtaining non-uniform joint spaces. The study uses finite element analysis and Cosserat continuum theory to gather appropriate results. The study reveals that average layer thickness for numerical analysis is needed for prediction of slope failures.

Abstract: Many interpretations of small-strain experiments indicate a non-linear dependence of soil stiffness on pressure. This shows that small-strain stiffness can be expressed as a power function of the mean effective stress rather than as a linear function of stress. Many cases in the field show the importance of these behaviours to load–deformation prediction in a soil-structure interaction problem. This paper presents a numerical implementation and validation of non-linear pressure-dependent stiffness in a hyperplasticity model using a strain-driven forward-Euler integration scheme. The kinematic hardening function was incorporated into a finite number of multiple-yield surfaces of Modified Cam Clay to characterise small-strain stiffness and accommodate smooth transition of stiffness corresponding to different loading conditions and stress histories. Experimental results of current state and loading history dependence in overconsolidated clay are compared to the model prediction. [Copyright &y& Elsevier]

Steel stiffened panels are widely used in engineering design and construction. However, numerical modeling and analysis effort for a three-dimensional (3D) stiffened panel may be notable, especially for the ultimate limit state of ship structures. Therefore, a homogenization method is outlined that transforms 3D stiffened panel into an Equivalent Single Layer (ESL) concerning the same mechanical behavior. ESL stiffnesses are obtained with a unit cell analyses based on stiffened panel where periodicity is imposed with boundary conditions based on a first-order shear deformation theory (FSDT). Stiffnesses were determined from the first derivative of a membrane force and bending moment obtained with numerical simulations. The effect of initial imperfection shape was included in the analysis to account for local and global buckling behavior. ESL with non-linear stiffness was implemented in Abaqus UGENS subroutine, allowing incremental evaluation of stiffness. Ultimate strength prediction of a steel grillage model with ESL finite element analysis was in excellent agreement with detailed 3D FEM analysis. The key in this analysis was consideration of non-linear ESL stiffness as linear analysis was unable to detect the point where ultimate strength capacity of the grillage was reached. • Homogenization method aims to transform the detailed 3D stiffened panel into an equivalent single layer (ESL). • Geometrical and material nonlinearities were considered in the stiffness calculation of ESL. • UGENS subroutine was invoked to involve the non-nonlinear membrane force and bending moment of ESL. • Ultimate strength of stiffened panel was accurately determined with current non-linear ESL approach. [ABSTRACT FROM AUTHOR]

Abstract: Over the last 10 years argillaceous rocks (mudrocks), such as the Jurassic claystone Opalinus Clay, have gained acceptance as a potential host formation for geological disposal of nuclear waste. Observations from tunnels in Opalinus Clay at the Mont Terri rock laboratory, Switzerland, suggest that the excavation-induced response is not linear-elastic. The micro-structure of the Opalinus Clay has been identified as a source for this response. It has been demonstrated that diagenetic processes over the last 180Ma have been responsible for the formation of strong diagenetic bonds locking latent strain energy into the micro-structure of Opalinus Clay. A conceptual model of the micro-structure, including the effects of diagenetic processes, has been developed as a framework to interpret the mechanical behaviour of the Opalinus Clay. Samples recovered at Mont Terri rock laboratory have been subjected to processes that have resulted in bond breakage and the release of locked-in latent strain energy. This tends to reduce the strength and deformation properties of samples and induces low stiffness non-linearity of the stress–strain curve at low stress levels. Numerical modelling of the sampling stress-path at Mont Terri rock laboratory shows that unloading was the dominant factor resulting in this response. As a result, samples can shed light on the unloading response of the rockmass to excavation. This non-linear behaviour has been quantified by means of routine laboratory compressive tests. [Copyright &y& Elsevier]

Abstract: In this paper we present a novel MEMS force sensor that exploits the post-buckling phenomenon of slender silicon columns. The design philosophy and fabrication process is discussed and analytical expressions for the force-displacement characteristics are developed. The sensor can be used to perform quantitative and qualitative measurements in-situ in SEM, TEM or STM, where the small chamber size makes it challenging to integrate conventional force-displacement sensors. Potential applications for the sensor are characterization of carbon nanotube-polymer interfaces, nanoscale thin film testing and mechanical testing of single biological cells. [Copyright &y& Elsevier]

The possibility of shifting sound energy from lower to higher frequency bands is investigated. The system configuration considered is a segmented structure having non-linear stiffness characteristics. It is proposed here that such a frequency-shifting mechanism could complement metamaterial concepts for mass-efficient sound barriers. The acoustical behavior of the material system was studied through a representative two-dimensional model consisting of a segmented plate with a contact interface. Multiple harmonic peaks were observed in response to a purely single frequency excitation, and the strength of the response was found to depend on the degree of non-linearity introduced. The lower and closer an excitation frequency was to the characteristic resonance frequencies of the base system, the stronger was the predicted higher harmonic response. The broadband sound transmission loss of these systems has also been calculated and the low frequency sound transmission loss was found to increase as the level of the broadband incident sound field increased. The present findings support the feasibility of designing material systems that transfer energy from lower frequency bands, where a sound barrier is less efficient, to higher bands where energy is more readily dissipated. [ABSTRACT FROM AUTHOR]