Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method

The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress, the modified couple stress theory （MCST）, and the nonlocal elasticity theories using the differential quadrature method （DQM） is presented. Main advantages of the MCST over the classical theory （CT） are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter. Based on the nonlinear von Karman assumption, the governing equations of equilibrium for the micro-classical plate consid- ering midplane displacements are derived based on the minimum principle of potential energy. Using the DQM, the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained. Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature. A parametric study is conducted to show the effects of the aspect ratio, the side-to-thickness ratio, Eringen＇s nonlocal parameter, the material length scale parameter, Young＇s modulus of the surface layer, the surface residual stress, the polymer matrix coefficients, and various boundary conditions on the dimensionless uniaxial, biaxial, and shear critical buckling loads. The results indicate that the critical buckling loads are strongly sensitive to Eringen＇s nonlocal parameter, the material length scale parameter, and the surface residual stress effects, while the effect of Young＇s modulus of the surface layer on the critical buckling load is negligible. Also, considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate. The results show that the critical biaxial buckling load increases with an increase in G12/E2 and vice versa for E1/E2. It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude. Because of the most lightweight micro-composite materials with high strength/weight and stiffness/weight ratios, it is anticipated that the results of the present work are useful in experimental characterization of the mechanical properties of micro-composite plates in the aircraft industry and other engineering applications.

Derivation of energy-based base shear force coefficient considering hysteretic behavior and P-delta effects

A modified energy-balance equation accounting for P-delta effects and hysteretic behavior of reinforced concrete members is derived. Reduced hysteretic properties of structural components due to combined stiffness and strength degradation and pinching effects, and hysteretic damping are taken into account in a simple manner by utilizing plastic energy and seismic input energy modification factors. Having a pre-selected yield mechanism, energy balance of structure in inelastic range is considered. P-delta effects are included in derived equation by adding the external work of gravity loads to the work of equivalent inertia forces and equating the total external work to the modified plastic energy. Earthquake energy input to multi degree of freedom（MDOF） system is approximated by using the modal energy-decomposition. Energybased base shear coefficients are verified by means of both pushover analysis and nonlinear time history（NLTH） analysis of several RC frames having different number of stories. NLTH analyses of frames are performed by using the time histories of ten scaled ground motions compatible with elastic design acceleration spectrum and fulfilling duration/amplitude related requirements of Turkish Seismic Design Code. The observed correlation between energy-based base shear force coefficients and the average base shear force coefficients of NLTH analyses provides a reasonable confidence in estimation of nonlinear base shear force capacity of frames by using the derived equation.

Nonlinear Stability of Plane Rotating Shear Flow under Three-Dimensional Nondivergence Disturbances

Nonlinear stability criterion for plane rotating shear flow under three-dimensional nondivergence disturbances was obtained by using both variational principle and convexity estimate introduced by Arnold (1965) and Holm et al. (1985). The results obtained in this paper show that the effect of Coriolis force plays an important role in the nonlinear stability criterion, and the nonlinear stability property of the basic flow depends on both the distribution of basic states and the way the external disturbance acts on the states. The upper bound of the gradient of the mass density displacement from the equilibrium k2 = is determined by the basic states and one example was given to show the exact upper value of k. The remarks on Blumen's paper were also given at Section 4 of this paper.

ON THE STABILITY OF DISTORTED LAMINAR FLOW(Ⅲ)—THE NONLINEAR STABILITY ANALYSIS OF DISTORTED PARALLEL SHEAR FLOW

Based on the hydrodynamic stability theory of distorted laminar flow and the kind of distortion profiles on the mean velocity in parallel shear flow given in paper [1], this paper investigates the nonlinear stability behaviour of parallel shear flow, carries on stability calculation taking account of the perturbations of background turbulence noise under certain assumption, and obtains some results in accordance qualitatively with those of experiment for plane Poiseuille flow and pipe Poiseuille flow.

GEOMETRICALLY NONLINEAR ANALYSIS OF MINDLIN PLATE USING THE INCOMPATIBLE BENDING ELEMENTS WITHIN TERNAL SH

An approach of the incompatible elements with additional internal shear strain is,in the presem paper,suggested and applied to geometrically nonlinear analysis of Mi-ndlin plate bending problem.It provides a quite covenient way to avoid the whear loc-king troubles.An energy consistency condition for this kind of C°elements is offered.The nonlinear element formulations and some numerical results are presented.