Latin American Journal of Solids and Structures, Volume: 9, Issue: 4, Published: 2012
• ## An accelerated incremental algorithm to trace the nonlinear equilibrium path of structures

Saffari, Hamed; Mirzai, Nadia M.; Mansouri, Iman

Abstract in English:

This paper deals with the convergence acceleration of iterative nonlinear methods. An effective iterative algorithm, named the three-point method, is applied to nonlinear analysis of structures. In terms of computational cost, each iteration of the three-point method requires three evaluations of the function. In this study the effective functions have been proposed to accelerate the convergence process. The proposed method has a convergence order of eight, and it is important to note that its implementation does not require the computation of higher order derivatives compared to most other methods of the same order. To trace the equilibrium path beyond the limit point, a normal flow algorithm is implemented into a computer program. The three-point method is applied as an inner step in the normal flow algorithm. The procedure can be used for structures with complex behavior, including: unloading, snap-through, elastic post-buckling and inelastic post-buckling analyses. Several numerical examples are given to illustrate the efficiency and performance of the new method. Results show that the new method is comparable with the well-known existing methods and gives better results in convergence speed.
• ## Novel equivalent function for deadzone nonlinearity: applied to analytical solution of beam vibration using He's Parameter Expanding Method

Sedighi, Hamid M.; Shirazi, Kourosh H.; Zare, Jamal

Abstract in English:

This study intends to introduce the novel and efficient exact equivalent function (EF) for well-known deadzone nonlinearity. To indicate the effectiveness of this EF, the nonlinear vibration of cantilever beam in presence of deadzone nonlinear boundary condition is studied. The powerful analytical method, called He's Parameter Expanding Method (HPEM) is used to obtain the exact solution of dynamic behavior of mentioned system. It is shown that one term in series expansions is sufficient to obtain a highly accurate solution. Comparison of the obtained solutions using numerical method shows the soundness of this analytical EF.
• ## Transient wave propagation phenomena at visco-elastic half-spaces under distributed surface loadings

Mesquita, E; Antes, H; Thomazo, LH; Adolph, M

Abstract in English:

This article analyzes the transient wave propagation phenomena that take place at 2D viscoelastic half-spaces subjected to spatially distributed surface loadings and to distinct temporal excitations. It starts with a fairly detailed review of the existing strategies to describe transient analysis for elastic and viscoelastic continua by means of the Boundary Element Method (BEM). The review explores the possibilities and limitations of the existing transient BEM procedures to describe dynamic analysis of unbounded viscoelastic domains. It proceeds to explain the strategy used by the authors of this article to synthesize numerically fundamental solutions or auxiliary states that allow an accurate analysis of transient wave propagation phenomena at the surface of viscoelastic half-spaces. In particular, segments with spatially constant and linear stress distributions over a halfspace surface are considered. The solution for the superposition of constant and discontinuous adjacent elements as well as linear and continuous stress distributions is addressed. The in uence of the temporal excitation type and duration on the transient response is investigated. The present study is based on the numerical solution of stress boundary value problems of (visco)elastodynamics. In a first stage, the solution is obtained in the frequency domain. A numerical integration strategy allows the stationary solutions to be determined for very high frequencies. The transient solutions are obtained, in a second stage, by applying the Fast Fourier Transform (FFT) algorithm to the previously synthesized frequency domain solutions. Viscoelastic effects are taken into account by means of the elastic-viscoelastic correspondence principle. By analyzing the transient solution of the stress boundary value problems, it is possible to show that from every surface stress discontinuity three wave fronts are generated. The displacement velocity of these wave fronts can be associated to compression, shear and Rayleigh waves. It is shown that the half-space transient displacement solutions present abrupt jumps or oscillations which can be correlated to the arrival of these wave fronts at the observation point. Such a detailed analysis connecting half-space transient responses to the wave propagation fronts in viscoelastic half-spaces have not been reported in the reviewed literature.
• ## An effective thickness proposal for strength evaluation of one-side pitted steel plates under uniaxial compression

Abstract in English:

This paper presents the results of an investigation into the post-buckling behaviour and ultimate strength of imperfect pitted steel plates used in ship and other marine-related structures. A series of elastic-plastic large deflection finite element analyses is performed on pitted steel plates. The effects of pitting corrosion on one side of the plates are introduced into the finite element models. The effects on plate compressive strength as a result of parametric variation of the pitting corrosion geometry are evaluated. A proposal on the effective thickness is concluded in order to estimate the ultimate strength and explore the post-buckling behaviour of pitted steel plates under uniaxial compression.
• ## Nonlocal continuum mechanics formulation for axial, flexural, shear and contraction coupled wave propagation in single walled carbon nanotubes

Narendar, S; Gopalakrishnan, S

Abstract in English:

This paper presents the effect of nonlocal scaling parameter on the coupled i.e., axial, flexural, shear and contraction, wave propagation in single-walled carbon nanotubes (SWCNTs). The axial and transverse motion of SWCNT is modeled based on first order shear deformation theory (FSDT) and thickness contraction. The governing equations are derived based on nonlocal constitutive relations and the wave dispersion analysis is also carried out. The studies shows that the nonlocal scale parameter introduces certain band gap region in all wave modes where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite or wave speed tends to zero. The frequency at which this phenomenon occurs is called the escape frequency. Explicit expressions are derived for cut-off and escape frequencies of all waves in SWCNT. It is also shown that the cut-off frequencies of shear and contraction mode are independent of the nonlocal scale parameter. The results provided in this article are new and are useful guidance for the study and design of the next generation of nanodevices that make use of the coupled wave propagation properties of single-walled carbon nanotubes.
• ## Experimental investigation on the yield behavior of Nomex honeycombs under combined shear-compression

Zhou, Zhiwei; Wang, Zhihua; Zhao, Longmao; Shu, Xuefeng

Abstract in English:

This paper presents an experimental investigation on the yield behavior of Nomex honeycombs under combined shearcompression with regard to out-of-plane direction. Four different types of specimens were designed in order to investigate the influence of in-plane orientation angle on the yield behavior of honeycombs under combined loads. Two different failure modes of honeycomb specimens, i.e. the plastic buckling and the extension fracture of cell walls, are observed under combined shear-compression. The experimental results validate that the in-plane orientation angle has a significant influence on the developments of the experimental yield surface. The experimental yield surfaces are compared with a phenomenological yield criterion capable of accounting for anisotropic behavior. The comparative analytical results indicate the experimental yield surfaces are approximately consistent with the theoretical yield surfaces in the normal-shear stress space. These experimental results are useful to develop constitutive models of Nomex honeycombs under combined shear-compression.
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