Narrow Results

This study aims to analyze the free vibration of an ogival arch in which two symmetrical arched shapes are discontinuously met at the mid-arc. Differential equations governing the free vibration of an ogival circular arch were derived, where the rotatory inertia and shear deformation effects are included. The governing equations were numerically solved to calculate natural frequencies and mode shapes. In numerical solution methods, the symmetric and anti-symmetric boundary conditions at the mid-arc were focused rather than the boundary conditions of supported end due to the discontinuity of the mid-arc. For the first time, the free vibration problem for discontinuous arches, such as ogival arches, is solved in this study. Calculation results of this study for natural frequencies are compared well with those of the finite element method. The effects of various arch parameters on natural frequencies were highlighted and discussed in detail.

This paper discusses two alternative formulations for developing orthotropic thick plate finite elements, namely the free formulation and the deviatoric strain formulation. These formulations are combined with interpolations for the transverse displacement and rotations that exactly satisfy the governing equations of Mindlin’s theory. Hence, the resulting element approximations are consistent for both thick and thin plates, and no locking occurs in the thin plate limit. The two formulations can be used to develop elements of arbitrary order and geometry, and several rectangular and triangular elements are derived in the paper. Examples are given in the paper to demonstrate the behavior and accuracy that is achieved with the proposed elements for both static and dynamics problems.

Equiatomic CoCrNi is a kind of medium-entropy alloy with excellent mechanical properties and wide application potentials in aerospace, nuclear energy, biomedical engineering, etc. In this paper, we investigate the effect of grain boundaries in CoCrNi under the shear loads through molecular dynamics (MD) simulations on 21 specially designed CoCrNi bicrystal specimens with symmetric tilt grain boundaries. The MD models of CoCrNi bicrystals were constructed and simulated using the open-source software LAMMPS. Shear loads parallel to the grain boundary plane were applied to the models after they reach equilibrium. Post-processing is conducted utilising the Common Neighbour Analysis (CNA) algorithm and Dislocation Extraction Algorithm (DXA). The stress–strain curves and microstructural evolution processes were analysed. According to the stress–strain curve and microstructural evolution characteristics, four types of deformation modes were identified, each corresponding to a specific range of misorientation angles. This study provides unique insights into the plastic deformation mechanisms of medium-entropy alloys.

The microstructure, pole figure and r-value of the frictionally rolled and subsequently heat treated AA 5052 Al sheets were investigated by optical microscopy, x-ray diffractometer and tensile tester, respectively. Frictionally rolled AA 5052 Al specimens showed a fine grain size. After subsequently heat treated specimens, the ND//<111> texture component was increased. The r-values of the frictionally rolled and subsequently heat treated Al alloy sheets were about two times higher than those of the original Al sheets. These could be related to the formation of ND//<111> texture components through frictional rolling in and subsequent heat treatment of AA 5052 Al sheet.

Cross-roll rolling of AA 5052 sheets was carried out using a rolling mill in which the roll axes are tilted by ±7.5° away from the transverse direction of the rolled sample. Besides cross-roll rolling, normal-rolling using a conventional rolling mill was also carried out with the same rolling schedule for clarifying the effect of cross-roll rolling. The evolution of strain states during cross-roll rolling was investigated by texture measurements and by three-dimensional finite element method (FEM) simulation. Cross-roll rolling gives rise to the operation of all three shear components ε ₁₂, ε ₁₃ and ε ₂₃ in the roll gap. This complex shear states during cross-roll rolling strongly reduce the intensities of the deformation texture components.

The objective of this paper is to apply He's homotopy perturbation method (HPM) to analyze nonlinear free vibration of simply supported Timoshenko beams considering the effects of rotary inertia and shear deformation. First, the equation governing the nonlinear free vibration of a Timoshinko beam is nondimensionalized. Galerkin's projection method is utilized to reduce the governing nonlinear partial differential equation to a nonlinear ordinary differential equation. HPM is then used to find analytic expressions for nonlinear natural frequencies of the pre-stretched beam. A parametric study has also been applied in order to investigate the effects of design parameters such as applied axial load and slenderness ratio. Comparison between presented results and numerical results which are in full agreement shows that HPM can significantly improve the accuracy of previously reported results in the literature.

Microstructural evolution and flow behavior of twin-roll cast AZ41 magnesium alloy during hot compression were characterized by employing deformation temperature of 300°C, 350°C and 400°C, and strain rate ranging from 10^-3 to 10^-2s^-1. When compressed at different temperature (300°C, 350°C and 400°C) and strain rate (10^-3 and 10^-2s^-1) all stress strain curves showed a flow softening behavior before strained to 0.51 due to dynamic recrystallization, even though concurrent twinning was quite active. Twinning contributed to the flow hardening behavior appeared during the end of hot compression (ε > 0.51) at a strain rate of 10^-2s^-1 and elevated temperature (300°C, 350°C and 400°C) in spite of the softening effect of concurrently occurred dynamic recrystallization. TEM image showed that discontinuous recrystallization occurred when deformed at elevated temperature as high as 400°C and the strain rate ranging from 10^-2 to 10^-3s^-1. It is suggested that dislocation slip, twinning and recrystallization develop in a cyclic mode from initial stage to the end of hot compression.

The effects of shear deformation at 1173 K on the mechanical properties and deformation mechanism of pure tungsten are investigated by molecular dynamics (MD). The results show that the shear deformation of pure tungsten is dominated by dislocation multiplication and slip band deformation. The shear angle has a significant effect on the mechanical properties of pure tungsten. The yield strength is 4.21 Gpa at a shear angle of 11${}^{\circ }$, and it increases significantly to 11.84 Gpa while the shear angle increasing to 27${}^{\circ }$. In the plastic deformation stage, the stress–strain curve shows obvious oscillation due to the interaction of dislocations in the single-crystal tungsten and the effect of strain strengthening. In addition, the evolution of dislocation and twining in the compression system against shear angle indicates the variation of deformation behavior. When the shear angle is 11${}^{\circ }$, the lengths of dislocation 1/2$〈111〉$ and $〈100〉$ increase to a peak rapidly, which illustrates dislocation strengthening. However, when the shear angle is more than 11${}^{\circ }$, the decrease of dislocation length and the appearance of twins along $〈111〉$ direction demonstrate the twining accompanied with dislocation tangling, resulting in the additional increase of strength.

In concentration gradient (CG) nano-polycrystalline Ni-Co alloy, the deformation mechanism of each region is different with the increase of Co content. It is found that in the Co-free region, grain boundary diffusion and dislocation slip mechanisms are dominant, while in other regions, there is a synergistic effect of solid solution strengthening. Moreover, the formation of new small grains by the migration of GB atoms will assist in the deformation of large grains, and the alloy exhibits gentle and stable stress–strain curve pattern. Meantime, although the dislocation density of each region is different, the dislocation density still changes stably before and after shearing. Compared with the uniform structure, the flow stress fluctuation is small when the CG structure is plastically deformed, which proves that this kind of structure is more stable. Moreover, it is found that at different temperatures, the CG alloy also shows stable dislocation density and coordination of various mechanisms, which ensures the strength stability. It is revealed that the CG structure has important properties that make the material strength more stable. This work demonstrates the excellent properties of CG alloy and has positive guiding significance for the development of low-cost, high-performance materials in terms of theoretical and practical applications.

Ni–Co alloy has great advantages in the fields of micro-electromechanical systems and aerospace, however, the lack of micro-deformation mechanism restricts its industrial application. Herein, the deformation mechanism and microstructure evolution of Ni–Co alloy nanoplate under shear loading are investigated by MD. The yield strength increases gradually with the increase of the velocity, and the highest shear modulus is 111.43 GPa. The stress concentration leads to the nucleation and expansion of the dislocation, and the stacking fault expands with the dislocation motion, swallowing most of the disordered atoms. By Dislocation Extraction Algorithm (DXA), it is found that Shockley and Perfect dislocations make a major role, and the interactions between dislocations are responsible for the high mechanical properties. As the temperature increases, the yield strength decreases significantly, the stress fluctuations in the plastic phase at 100 K and 200 K are greater compared to other temperatures. Meanwhile, the coherence of the dislocations motion decreases, and the atoms in the stacking faults are scattered, leading to the decreasing of area. The above results are helpful for the design and control of nanoelectronic facilities and provide a significant guide for the industrial applications of Ni–Co alloy nanoplate.

The lack of a bandgap in stanene severely limits its outstanding characteristics in optoelectronic devices. Using first-principles calculations, we systematically investigate the effects of full hydrogenation and shear deformation on the electronic structure and optical properties of stanene. Hydrogenation exerts a remarkable impact on electronic structure of stanene, enabling surface state transition from quasi-metallic to semiconducting. Shear degrades the structural stability of full-hydrogenated stanene (FHstanene). FHstanene exhibits a tunable bandgap of 1.327eV, which can be further reduced to 0.719eV through shear deformation. The presence of spin-orbit coupling (SOC) induces band splitting in FHstanene. The maximum optical absorption of FHstanene occurs at 291nm, while the reflectance peak is observed at 449nm. The variation in bandgap due to deformation results in a redshift in the absorption coefficient and reflectance, and shear deformation increases the reflectance of FHstanene. These findings broaden the application prospects of stanene in novel nano-optoelectronic devices.

The coupled free vibration analysis of the thin-walled laminated composite I-beams with bisymmetric and monosymmetric cross sections considering shear effects is developed. The laminated composite beam takes into account the transverse shear and the restrained warping induced shear deformation based on the first-order shear deformation beam theory. The analytical technique is used to derive the constitutive equations and the equations of motion of the beam in a systematic manner considering all deformations and their mutual couplings. The explicit expressions for displacement parameters are presented by applying the power series expansions of displacement components to simultaneous ordinary differential equations. Finally, the dynamic stiffness matrix is determined using the force–displacement relationships. In addition, for comparison, a finite beam element with two-nodes and fourteen-degrees-of-freedom is presented to solve the equations of motion. The performance of the dynamic stiffness matrix developed by study is tested through the solutions of numerical examples and the obtained results are compared with results available in literature and the detailed three-dimensional analysis results using the shell elements of ABAQUS. The vibrational behavior and the effect of shear deformation are investigated with respect to the modulus ratios and the fiber angle change.

The free in-plane vibration of a shallow circular arch with uniform cross-section is investigated by taking into account axial extension, shear deformation and rotatory inertia effects. The exact solution of the governing differential equations is obtained by the initial value method. By employing the same solution procedure, the solutions are also given for the other cases, in which each effect is considered alone, as well as no effect. The frequency coefficients are obtained for the lowest five vibration modes of arches with five combinations of classical boundary conditions, and various slenderness ratios and opening angles. The results show that the shear deformation and rotatory inertia effects are also very important as well as the axial extension effect, even if a slender shallow arch is considered. The discrepancies among the results of the five cases decrease, when opening angle increases for a constant radius and slenderness ratio. The effects of the boundary conditions and the slenderness ratio of the arch are investigated. The discrepancies among the results of the cases become much more important in higher modes. The mode shapes of a shallow arch are obtained for each case.

The governing differential equations for the out-of-plane, free vibration of circular curved beams resting on elastic foundations are derived and solved numerically. The formulation takes into consideration the effects of rotary inertia and transverse shear deformation. The lowest three natural frequencies are calculated for beams with hinged–hinged, hinged-clamped, and clamped–clamped end constraints. The effects of various system parameters as well as rotary inertia and shear deformation on the natural frequencies are investigated.

A triangular element based on Reddy's higher order shear deformation theory is developed for free vibration analysis of composite plates. In the Reddy's plate theory, the transverse shear stress varies in a parabolic manner across the plate thickness and vanishes at the top and bottom surfaces of the plate. Moreover, it does not involve any additional unknowns. Thus the plate theory is quite simple and elegant. Unfortunately, such an attractive plate theory cannot be exploited as expected in finite element analysis, primarily due to the difficulties in satisfying the inter-element continuity requirement. This has inspired us to develop the present element, which has three corner nodes and three mid-side nodes with the same number of degrees of freedom. To demonstrate the performance of the element, numerical examples of isotropic and composite plates under different situations are solved. The results are compared with the analytical solutions and other published results, which show the accuracy and range of applicability of the proposed element in the problem of vibration analysis.

The differential equations governing free vibrations of the elastic, parabolic arches with unsymmetric axes are derived in Cartesian coordinates rather than in polar coordinates. The formulation includes the effects of axial extension, shear deformation and rotatory inertia. Frequencies and mode shapes are computed numerically for arches with clamped-clamped, clamped-hinged, hinged-clamped and hinged-hinged ends. The convergent efficiency is highly improved under the newly derived differential equations in Cartesian coordinates. The lowest four natural frequency parameters are reported as functions of four non-dimensional system parameters: the rise to chord length ratio, the span length to chord length ratio, the slenderness ratio and the shear parameter. Typical mode shapes of vibrating arches are also presented.

The postbuckling behavior of beams on a two-parameter elastic foundation subjected to axial forces is investigated. Based on the strain energy expression, a two-node nonlinear beam element is formulated. The element includes the effects of shear deformation, foundation deflection in both the horizontal and vertical directions. The bracketing procedure and the iterative Newton–Raphson method with arc-length control technique are adopted to compute the critical loads and equilibrium paths of the beams with various boundary conditions. The numerical results show that the critical load and the postbuckling behavior are not only governed by the foundation stiffness, but by the foundation deflection in the horizontal direction also. The postbuckling characteristics of the beams are altered by ignoring the foundation deflection in the horizontal direction. A detail investigation is carried out to highlight the influences of the partial support by the foundation and the beam slenderness on the critical load and the postbuckling behavior.

This paper deals with the geometrical nonlinear analyses of buckled columns. Differential equations governing the elasticas of buckled columns are derived, in which both the effects of taper type and shear deformation are included. Three kinds of taper types are considered, i.e. breadth, depth and square tapers. Differential equations are solved numerically to obtain the deflection of elasticas and the buckling loads of such columns. Both clamped ends and hinged ends are considered. The effects of shear deformation on the deflection of elasticas of buckled columns and on the buckling loads of columns are investigated extensively. The buckling load equations for uniform columns are expressed as a function of the implicit shear effect. Experimental studies are presented that complement the theoretical results of nonlinear responses of the elasticas.

In this paper, we consider the nonlinear analysis of frames with shear deformation, and present a series of benchmark solutions for a variety of problems and modelling assumptions. The benchmarks enable users and developers of nonlinear analysis software to test the accuracy of their procedures when including shear deformation.

This paper presents the incorporation of shear deformation effects into a Generalized Beam Theory (GBT) developed to analyze the structural behavior of composite thin-walled columns made of laminated plates and displaying arbitrary orthotropy. Unlike other existing beam theories, the present GBT formulation incorporates in a unified fashion (i) elastic coupling effects, (ii) warping effects, (iii) cross-section in-plane deformation and (iv) shear deformation. The main concepts and procedures involved in the available GBT are adapted/modified to account for the specific aspects related to the member shear deformation. In particular, the GBT fundamental equilibrium equations are presented and their terms are physically interpreted. An I-section is used to illustrate the performance of GBT cross-section analysis and the mechanical properties are explained in detail. With the purpose of solving the GBT system of differential equilibrium equations, a finite element formulation is briefly presented. Finally, in order to clarify the concepts involved in the formulated GBT and illustrate its application and capabilities, the linear (first-order) and stability behavior of three composite I-section members displaying non-aligned orthotropy are analyzed and the results obtained are thoroughly discussed and compared with estimates available in the literature.