Showing papers on "Bending moment published in 2019"

Nonlocal strain gradient exact solutions for functionally graded inflected nano-beams

Abstract: The size-dependent bending behavior of nano-beams is investigated by the modified nonlocal strain gradient elasticity theory. According to this model, the bending moment is expressed by integral convolutions of elastic flexural curvature and of its derivative with the special bi-exponential averaging kernel. It has been recently proven that such a relation is equivalent to a differential equation, involving bending moment and flexural curvature fields, equipped with natural higher-order boundary conditions of constitutive type. The associated elastostatic problem of a Bernoulli-Euler functionally graded nanobeam is formulated and solved for simple statical schemes of technical interest. An effective analytical approach is presented and exploited to establish exact expressions of nonlocal strain gradient transverse displacements of doubly clamped, cantilever, clamped-simply supported and simply supported nano-beams, detecting thus also new benchmarks for numerical analyses. Comparisons with results of literature, corresponding to selected higher-order boundary conditions are provided and discussed. The considered nonlocal strain gradient model can be advantageously adopted to characterize scale phenomena in nano-engineering problems.

Nonlinear dynamic response of sandwich beams with functionally graded negative Poisson’s ratio honeycomb core

Abstract: This paper investigates the nonlinear dynamic response of sandwich beams with functionally graded (FG) negative Poisson’s ratio (NPR) honeycomb core in thermal environments. The novel constructions of sandwich beams with four FG configurations of re-entrant honeycomb cores through the beam thickness direction are proposed for the first time. The temperature-dependent material properties of both face sheets and core of the sandwich beam are considered. 3D full scale finite element analyses are conducted to investigate the nonlinear dynamic response, and the variation of effective Poisson’s ratio (EPR) of the sandwich beam in the large deflection region. The numerical simulations are carried out for the sandwich beam with FG-NPR honeycomb core, from which results for the same sandwich beam with uniform distributed NPR honeycomb core are obtained as a comparator. Present results indicate that, when subjected to transverse dynamic pressure, the induced dynamic bending moment of the sandwich beam with core of positive EPR is much bigger than that of the sandwich beam with NPR core, and the thickness of which will extraordinarily increase. The effects of loading types, functionally graded configurations, temperature changes, boundary conditions, and length-to-thickness ratios on the deflection-time curves and EPR-deflection curves of sandwich beams are discussed in detail.

Model tests of the response of landslide-stabilizing piles to piles with different stiffness.

Abstract: The deformation characteristics of landslides, reinforced by piles having different stiffness, are examined using physical model tests. Taking the Majiagou landslide and its pile system as a real prototype, and using a model test bed with 57-cm-long test piles made of reinforced concrete and polyesteramide to simulate rigid and flexible piles, the displacements of two physical models were monitored during progressive loading to simulate the landslide-stabilizing pile system. The results indicate that (1) the bending moment of the rigid piles showed a reverse S pattern, peaking at the pile head; (2) the bending moment of the flexible piles developed a triangular pattern, peaking at the middle and lower parts of the pile; (3) the relative displacements of the landslide and piles during loading disclose four evolutionary stages, termed initial, coordinated, uncoordinated deformation, and failure; (4) the flexible pile system has a longer coordinated action stage but a shorter uncoordinated stage, than the system constructed with rigid piles. Finally, (5) the rigid piles exert an excellent control of soil deformation upslope of the piles, but it is easier for the landslide to slip over the pile heads. The results provide fundamental data for evaluating the long-term performance of the landslide–pile systems constructed with piles having different rigidity.

Nonlinear structural stability performance of pressurized thin-walled FGM arches under temperature variation field

Abstract: This paper focuses on the elastic structural stability analysis of the pressurized thin-walled functionally graded material (FGM) arches under temperature variation field. The material properties are temperature-dependent and thermo-elastic. The total potential energy function of the pinned–pinned arch was expressed explicitly by employing the classical thin-walled arch theories and admissible radial displacement functions. By means of the variational principle, the expressions of the critical buckling pressure were obtained analytically and verified numerically by developing a two-dimensional (2D) simulated model. The pre- and post-buckling equilibrium paths were depicted to explore the maximum pressure (buckling pressure). The comparison showed that the numerical results were in excellent agreement with the analytical solutions for different subtended angles, volume fraction exponents and temperature variations. In the end, the effects of volume fraction exponent and temperature variation were examined on the critical buckling pressure, the bending moment, the hoop force, the hoop strain and stress, the hoop and radial displacement components through the whole arch.

Material distribution optimization of functionally graded arch subjected to external pressure under temperature rise field

Abstract: This paper investigates the material spatial redistribution optimization of the conventional functionally graded material (CFGM) arch. An inverted functionally graded material (IFGM) arch is developed to promote the critical buckling pressure of the heated arch without variation of the volume portion of the material constituents of the CFGM arch. Based on the classical thin-walled arch theories and admissible displacement functions, the total potential energy function of the IFGM arch is obtained. By variation of this energy function, the non-linear bifurcation equilibrium equations are established, and the analytical prediction of the critical buckling pressure is obtained for the IFGM arch. Subsequently, a two-dimensional (2D) finite element model (FEM) is established to trace the pressure-displacement equilibrium paths to obtain the maximum pressure (critical buckling pressure). The numerical results show very close agreement with the present analytical solutions. Furthermore, the IFGM arch shows a substantial increase of the critical buckling pressure compared with the CFGM arch. In addition, the critical buckling pressure of the heated homogeneous arch is compared with the available other closed-form expressions. Finally, to further understand the stability of the pressurized IFGM arch under temperature rise field, parametric studies are performed to examine the effects of the various involved parameters, such as the volume fraction exponent and temperature rise on the bending moment, the hoop force, the hoop strain and stress, the radial and hoop displacement through the arch span.

Shear behavior of steel I-girder with stiffened corrugated web, Part I: Experimental study

Abstract: The shear stability of steel webs near the support section for long-span composite girders with corrugated steel webs is one of the main control factors for structural safety, which should be paid special attention to. Generally, concrete is poured on the inner side of corrugated steel webs to improve its shear stability, but encased concrete increases the weight of the girder, raises the difficulty of the construction process, and reduces the efficiency of the prestressing application. This paper proposes a new type of stiffened corrugated steel webs at the support area by adopting vertical or/and horizontal stiffeners instead of encased concrete. In order to explore the shear performance of proposed stiffened corrugated steel webs, experimental and numerical investigations were carried out in the present paper and the companion paper [1] , respectively. Four steel I-girders with corrugated webs considering different stiffener arrangements were designed and tested under shear loading. The failure modes, shear strength and stiffness, strain distributions were obtained and analyzed in detail. The test results show that all specimens failed due to interactive shear buckling of corrugated steel web; shear buckling occurred between horizontal stiffeners and bottom flange for horizontal stiffened corrugated steel webs, but extended to the entire height for vertical stiffened corrugated steel webs, the stiffeners distorted associated with the deformation of corrugated steel web. Shear strength of corrugated steel webs can be improved by vertical and horizontal stiffeners. The vertical stiffeners do not affect the “accordion effect” of corrugated steel webs, but the horizontal stiffeners increase the axial stiffness of corrugated steel web in local area and resist bending moment together with top and bottom flanges. The shear strain of stiffened corrugated steel web still distributes uniformly along the height of the web. All the experimental results are then employed in the companion paper for the validation of finite element method and the evaluation of existing analytical models for predicting shear strength of un-stiffened and stiffened corrugated steel webs.