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This paper presents a novel approach to the analysis of large deflection and post-buckling behavior of cantilever nanorods under different load conditions. The proposed approach utilizes a variational method, incorporating the Gurtin–Murdoch surface elasticity theory and the consistent couple stress theory to account for size-dependency effects. By accounting for the strain energy contributions of the bulk material, surface layer, and load conditions, this approach expresses the behavior of the nanorods in terms of their intrinsic coordinates. A finite element method was used to solve this numerical problem, generating a system of non-linear equations that were iteratively solved using the Newton–Raphson method. The results obtained from the finite element method were confirmed by those from the shooting method. Also, it highlights the effectiveness of the variational model in predicting the large deflection and post-buckling behavior of cantilever nanorods while considering both surface stress and couple stress effects. Furthermore, the study investigated the influence of surface stress and couple stress on the response of the nanorods to point and uniform loads. The results showed that incorporating both effects enhanced the stiffness of the nanorods compared to scenarios in which these effects were neglected. In addition, the couple stress effect was found to have a greater influence on the stiffening of nanorods for the same value of unitless parameters compared to surface stress effects. These findings offer valuable insights into the large deflection and post-buckling behavior of cantilever nanorods and highlight the importance of surface stress and couple stress effects. The model proposed in this study has potential applications in advanced technological device designs by providing a comprehensive understanding of the mechanical response of nanorods, allowing for more accurate predictions and enhanced device performance. [ABSTRACT FROM AUTHOR]

This paper focuses on the analytical procedure for determining novel exact expressions for internal forces and displacements of hemi-ellipsoidal shells formed as an axisymmetric shell of revolution under uniformly distributed load such as imposed loads. The simplest form of expressions for solutions is derived based on the linear membrane theory under symmetrical loading that is formed as a shell of revolution. The results have been validated and have a good consistency with numerical solutions from the finite-element method (FEM) which are derived based on the principle of virtual work and differential geometry. The obtained analytical exact solution is only valid for small displacements or if the response does not exceed the linearity limit. In cases of large displacements, geometrical nonlinear finite-element analysis is recommended to determine the solution. The linearity limit determination is demonstrated, and the effects of shells' geometry, thickness, and magnitude of applied loads are presented. Additionally, the linear buckling analysis has been performed. The study found that the size ratio, thickness, and support condition have a significant effect on the critical load of the first mode, and the hemispherical shells have the highest buckling resistance due to the geometry. [ABSTRACT FROM AUTHOR]

This study investigates the elastic buckling behavior of oblate hemi-ellipsoidal shells (OHES) subjected to non-uniform external hydrostatic pressure. The virtual work-energy of OHES consists of virtual strain energy due to membrane, bending, in-plane stress resultants, and virtual work of hydrostatic pressure. For buckling analysis, the geometric stiffness matrix is obtained from the strain energy due to in-plane stress resultants. A finite element procedure via a C1 continuity axisymmetric element is applied to solve the critical hydrostatic pressure from the eigenvalue buckling problem. The buckling pressure of the hemi-ellipsoidal dome subjected to uniform external pressure is verified with the previous research and FEM commercial software. Present results also indicate that the maximum in-plane stress of the hemi-ellipsoidal shell shapes are near the apex point as the axisymmetric buckling shape. In the case of hydrostatic pressure, the critical hydrostatic pressure of OHES is determined and are in good agreement when compared with the experimental results in published research. Furthermore, the shape ratio influences the difference in critical load results between uniform pressure and hydrostatic pressure, especially when the shape ratio is higher than 0.5 and the a / t ratio is less than or equal to 100. Seawater depth limitations in subsea engineering are also presented and found that the shell thickness and shape ratio are the major factors affecting critical seawater depth. [ABSTRACT FROM AUTHOR]

In this paper, buckling of a nanowire column subjected to self-weight and tip load is investigated. One end of the nanowire is free, while the other end is attached to a rotational spring support. Considering the equilibrium equations together with the Euler–Bernoulli beam theory, the governing differential equation describing the behavior of the column can be obtained. Effect of surface stress is also incorporated into the formulations in terms of transverse distributed loading. The differential equation has been solved analytically and the general solution can be presented in the terms of Bessel function of the first kind. Applying the boundary conditions, the characteristic equations influenced by surface stress and stiffness of the rotational spring at the support can be expressed and then the critical load can be determined using the Newton–Raphson iterative scheme. From the results, they reveal that the positive surface stress could strengthen the nanowire against the buckling. Fixity at the base is also influenced to the critical load where the increase of the stiffness of the spring results in the increase of critical load as well. [ABSTRACT FROM AUTHOR]

This paper investigates the behavior of a pre-stressed arch under a sliding load, where the initial configuration can be obtained from the buckling of a straight column. The shape of the pre-stressed arch can be varied by increasing the end shortening. Subsequently, a sliding load is applied at a certain height level. The orientation of the applied load maintains the right angle with respect to the tangential line of the arch. By moving the load horizontally, the behavior of the arch can be explored. The governing differential equations of the problem can be obtained by equilibrium equations, constitutive relation, and nonlinear geometric expressions. The exact closed-form solutions can be derived in terms of elliptic integrals of the first and second kinds. In this problem, the arch can be divided into two segments where each segment is a part of a buckled hinged-hinged column mounted on an inclined support. The shooting method is employed to solve the numerical solutions for comparing with the elliptic integral method. The stability of the pre-stressed arch is evaluated from vibration analysis, where the shooting method is again utilized for solving the natural frequencies in terms of a square function. A simple experiment is set up to explore the equilibrium shapes. Poly-carbonate sheet is utilized as the pre-stressed arch. From the results, it is found that the results obtained from elliptic integral method are in excellent agreement with those obtained from shooting method. The equilibrium shapes from the theoretical results can also compare with those from the experiment. The pre-stressed arch can lose its stability and snap into an upside-down (inverted) configuration depending on the ratio of rise to span-length and loading height. The instability of the arch is not only detected during the pushing of the sliding load but a pulling load can also cause unstable behavior of the arch. [ABSTRACT FROM AUTHOR]

This research studies the potential of using disposed fly ash to add up or partially replace Portland cement Type I in ground improvement by cement column technique. The strength characteristic of cement-fly ash admixed Bangkok clay was investigated by means of a series of unconfined compression tests, paying special attention to the influence of ground fly ash in this mixture. From testing results, the unconfined compressive strength and elastic modulus improved with an increasing of fly ash content. With the cement portions of greater than or equal to 10%, ground disposed fly ash could be employed as a pozzolanic material for partial replacement of cement in cement column construction. Based on the equivalent cementitious material content concept, an empirical equation relating the efficiency factor, a with mixing proportions was proposed. Then, together with this proposed efficiency factor, strength prediction of cement-fly ash admixed clay by Feret's equation and Abram's law were carried out and discussed. CE Database subject headings: Compressive strength; Cement; Fly ash; Water content; Clays; Concrete admixtures. Author keywords: Unconfined compressive strength; Cement admixed clay; Fly ash; Equivalent cementitous material content; Efficiency factor. DOI: 10.1061/(ASCE)0899-1561 (2010)22:1(49)