Explore the vast range of titles available.

This study has presented an improved method for determining physical nonlinearities of weakly nonlinear spring-suspension system and successfully applied to a novel hybrid aeroelastic–pressure balance (HAPB) system used in wind tunnel, which can be used for simultaneously obtaining the unsteady wind pressure and aeroelastic response of a test model. A nonlinear identification method of equivalent linearization approximation was firstly developed on the basis of the averaging method of Krylov–Bogoliubov to model the physical nonlinearity of a weakly nonlinear system. Subsequently, the nonlinear physical frequency and damping were identified using a modified Morlet wavelet transform method and a constant variant method. Using these methods, the physical nonlinear frequency and damping of the HAPB system with a vertical test model were determined and were validated by a time domain method and the Newmark - β method. Finally, the nonlinear mechanical frequency and damping of the HAPB system with inclined test models were determined in a similar way. This study has not only provided an identification method for determining physical nonlinearities of weakly nonlinear system, but presented the detail for developing a hybrid aeroelastic–pressure balance used in wind tunnel.

The article presents the results of a numerical study of the composite action of concrete and reinforcement in reinforced concrete flooring under emergency loads, taking into account physical and geometric nonlinearities. The study used a nonlinear static method in the LS-DYNA software package, which implements the Continuous Surface Cap Model (CSCM). The simulation model of a monolithic beam floor uses volumetric finite elements for concrete and rod elements for reinforcement. Isofields and graphs of the intensity of stresses and strains in the upper and lower reinforcement, as well as in the concrete at the floor elevation, with an increase in the vertical uniformly distributed load, were built. The load-bearing capacity of the monolithic slab under consideration was determined using the non-collapse criterion. The LS-DYNA software package makes it possible to study the action of load-bearing concrete structures modeling direct concrete reinforcement using reinforcing bars at a significantly nonlinear nature of strain.

In this paper, the nonlinear dynamic behaviors, especially, limit cycles and chaos, are investigated for the spherical shell composed of a class of visco-hyperelastic materials subjected to uniform radial loads at its inner and outer surfaces. To include the thickness effect, a more general model compared with the membrane and thin plate is proposed to investigate the dynamic characteristics of the visco-hyperelastic structure. Then, the coupled integro-differential equations describing the radially symmetric motion of the spherical shell are derived in terms of the variational principle and the finite viscoelasticity theory. Due to both the geometrical and physical nonlinearities, there exists an asymmetric homoclinic orbit for the hyperelastic structure. Particularly, under constant loads, the system converges to a stable equilibrium point, and the convergence position and speed are closely related to both the initial condition and the viscosity because of the existence of different basins, while under periodic loads, some complex phenomena, such as the limit cycles and chaos, are found, and the chaotic phenomena are analyzed by the bifurcation diagram and Lyapunov exponent. Moreover, by numerical analyses, parametric studies are carried out to illustrate the effects of viscosity, load amplitude, external frequency and initial condition.

The paper concerns the computations of mast guys taking into account both geometric and physical nonlinearities. Experimental studies have been conducted, the aim of which was to determine σ - ε (stress – deformation) relation for steel rope and to determine the value of modulus of elasticity after its pre-stretching. Results of the research were used to create appropriate computational cable models within the elastic and inelastic range in SOFiSTiK software, based on FEM. The computational cable models were then used to perform parametric analyses of single cables with horizontal and diagonal chords and computations of a lattice guyed mast. The computational single cables results obtained in the SOFiSTiK software were confronted with the results obtained by the analytical method, based on the cable equation. The FEM analyses performed for single cables have proven usefulness of presented analytical procedure for computation of structures with cable elements (e.g. guyed masts) taking into account both the geometric and physical nonlinearity of the cables. It has been shown that while using steel ropes without pre-stretching, permanent deformations in the cables may occur, which affect the shape of the cable and may significantly reduce values of forces in the cables. This phenomenon can be particularly dangerous in the case of guyed masts, as it may affect the reduction in rigidity of the mast structure.

A mathematical model of a contact interaction between two plates made from materials with different elasticity modulus is derived taking into account physical and design nonlinearities. In order to study the stress–strain state of this complex mechanical structure, the method of variational iteration has been employed allowing for reduction of partial differential equations to ordinary differential equations (ODEs). The theorem regarding convergence of this method is formulated for the class of similar-like problems. The convergence of the proposed iterational procedure used for obtaining a solution to contact problems of two plates is proved. In the studied case, the physical nonlinearity is introduced with the help of variable parameters associated with plate stiffness. The work is supplemented with a few numerical examples. Both Fourier and Morlet power spectra are employed to detect and analyse regular and chaotic vibrations of two interacting plates.

In this paper, the problem of bending a multilayered concrete rod of constant cross-section under quasi-static loads is considered. It is assumed that if the strain is below the elastic limit, the rod is deformed elastically, and if the strain is above the elastic limit, the rod is deformed nonlinearly quasi-elastically. It is assumed that the rod is in a uniaxial stress state.The calculations are obtained for a hinged rod in the case that the neutral line coincides with the axis of the rod. The analytical ratios are obtained to determine the limit loads for various locations of the boundary between the elastic and nonlinear quasi-elastic deformation areas in the case when the number of layers is two. The ratios are presented for determining the boundary between these areas.

Existing experimental data demonstrate a significant stress-state sensitivity of the properties for a wide class of solids, including metals, rocks, plastics, and other structural materials. Conventional parameters used to describe the material stress state are the stress triaxiality and the Lode angle. However, only dependence of the fracture criteria on the type of stress state is often considered. In the present paper, a version of constitutive relations is proposed which allow to describe the stress-state dependence of the material properties for the entire deformation process and thus to provide a more accurate approach to the estimation of the stress–strain state of solids. The proposed approach is exemplified with the solutions of various spherically symmetry problems for physically nonlinear solids. It can be noticed that the stress-state sensitivity taken into account may result in essential deviations of the solutions obtained from the predictions of the classical models. Although the constitutive relations are essentially nonlinear, in some particular cases, an analytic solution of the problem can be obtained. The approach discussed in this paper provides a relatively simple but realistic continuum model able to describe complicated deformation features of materials.

A mathematical model of contact interaction between two plates is presented, considering certain types of nonlinearity of each of the plates. Stress–strain state (SSS) of the interacting structural members is analyzed by the method of variational iterations, and the theorem of convergence of this method is provided. An iterative procedure for solving contact problems is developed and its convergence is also proved. Physical nonlinearity is considered by means of the method of variable parameters of elasticity. The SSS of a two-layer system of rectangular plates, depending on a type of boundary conditions as well as distances between plates, is investigated and supplemented with stress–strain curves σ i ( i ) ( e i ( i ) ) for each of the plates.

See the retraction notice E3S Web of Conferences 538 , 00001 (2024), https://doi.org/10.1051/e3sconf/202453800001

A new numerical-analytical method was developed to solve physically nonlinear deformation problems for axisymmetrically loaded irregular bodies of rotation with stress state-dependent characteristics. The problem was linearized by the parameter-based continuous extension method. For the variational formulation of the linearized problem, the Lagrangian functional was constructed, given by kinematically admissible displacement rates. For finding the basic unknowns of the nonlinear deformation problem, the Cauchy problem for the system of ordinary differential equations was formulated and solved by the Runge-Kutta–Merson method with the automatic step choice. The initial conditions were established by solving the linear elastic deformation problem. The right-hand sides of the differential equations at the fixed load parameters corresponding to the Runge-Kutta–Merson scheme were calculated from the solution of the variational problem for the Lagrangian functional. The variational problems were solved by the Ritz method in combination with the method of Rfunctions. The latter can present an approximate solution in the form of a formula, viz a solution structure that exactly satisfies all (general structure) or part (partial structure) of the boundary conditions. The nonlinear elastic deformation of a thick-walled straight cylinder and an irregular rotation body was investigated. The geometry effect on the stress-strain state was studied. Neglect of the different material behaviors in tension and compression was shown to involve tangible errors in the results of calculating the stress-strain state parameters.