Out-of-plane elastic buckling load and strength design of space truss arch with a rectangular section

The out-of-plane stability of the two-hinged space truss circular arch with a rectangular section is theoretically and numerically investigated in this paper.Firstly,the flexural stiffness and torsional stiffness of space truss arches are deduced.The calculation formula of out-of-plane elastic buckling loads of the space truss arch is derived based on the classical solution of out-of-plane flexural-torsional buckling loads of the solid web arch.However,since the classical solution cannot be used for the calculation of the arch with a small rise-span ratio,the formula for out-of-plane elastic buckling loads of space truss arches subjected to end bending moments is modified.Numerical research of the out-of-plane stability of space truss arches under different load cases shows that the theoretical formula proposed in this paper has good accuracy.Secondly,the design formulas to predict the out-of-plane elastoplastic stability strength of space truss arches subjected to the end bending moment and radial uniform load are presented through introducing a normalized slenderness ratio.By assuming that all components of space truss circular arches bear only axial force,the design formulas to prevent the local buckling of chord and transverse tubes are deduced.Finally,the bearing capacity design equations of space truss arches are proposed under vertical uniform load.

STUDIES ON THE TORSIONAL BUCKLING OF ELASTIC CYLINDRICAL SHELLS

The experimental phenomenon and theoretical analysis are given for the torsional buckling of elastic cylindrical shells. From the experiment, it is found that the postbuckling deformation doesn't occupy the whole length when the shell is longer. In the theoretical calculation, only the normal displacement boundary condition is taken into account. By comparing the present calculation results with the accurate result of Yamakis theory and the results of the present experiment, it is shown that the influence of the axial and circumference boundary condition is less important.

A simple criterion for finite time stability with application to impacted buckling of elastic columns

The existing theories of finite-time stability depend on a prescribed bound on initial disturbances and a prescribed threshold for allowable responses. It remains a challenge to identify the critical value of loading parameter for finite time instability observed in experiments without the need of specifying any prescribed threshold for al- lowable responses. Based on an energy balance analysis of a simple dynamic system, this paper proposes a general criterion for finite time stability which indicates that finite time stability of a linear dynamic system with constant coefficients during a given time interval [0, tf] is guaranteed provided the product of its maximum growth rate （determined by the maximum eigen-root pl 〉0） and the duration tf does not exceed 2, i.e., pltf 〈2. The proposed criterion （pltf=2） is applied to several problems of impacted buckling of elastic columns： （i） an elastic column impacted by a striking mass, （ii） longitudinal impact of an elastic column on a rigid wall, and （iii） an elastic column compressed at a constant speed （＂Hoff problem＂）, in which the time-varying axial force is replaced approximately by its average value over the time duration. Comparison of critical parameters predicted by the proposed criterion with available experimental and simulation data shows that the proposed criterion is in robust reasonable agreement with the known data, which suggests that the proposed simple criterion （pltf---2） can be used to estimate critical parameters for finite time stability of dynamic systems governed by linear equations with constant coefficients.

Static and dynamic snap-through behaviour of an elastic spherical shell

The deformation and snap-through behaviour of a thin-walled elastic spherical shell statically compressed on a flat surface or impacted against a fiat surface are studied the- oretically and numerically in order to estimate the influence of the dynamic effects on the response. A table tennis ball is considered as an example of a thin-walled elastic shell. It is shown that the increase of the impact velocity leads to a variation of the deformed shape thus resulting in larger de- formation energy. The increase of the contact force is caused by both the increased contribution of the inertia forces and contribution of the increased deformation energy. The contact force resulted from deformation/inertia of the ball and the shape of the deformed region are calcu- lated by the proposed theoretical models and compared with the results from both the finite element analysis and some previously obtained experimental data. Good agreement is demonstrated.

Influence of the connecting condition on the dynamic buckling of longitudinal impact for an elastic rod

The stress wave propagation law and dynamic buckling critical velocity are formulated and solved by considering a general axial connecting boundary for a slender elastic straight rod impacted by a rigid body. The influence of connecting stiffness on the critical velocity is investigated with varied impactor mass and buckling time. The influences of rod length and rod mass on the critical velocity are also discussed. It is found that greater connecting stiffness leads to larger stress amplitude, and further results in lower critical velocity. It is particularly noteworthy that when the connecting stiffness is less than a certain value, dynamic buckling only occurs before stress wave reflects off the connecting end. It is also shown that longer rod with larger slenderness ratio is easier to buckle, and the critical velocity for a larger-mass rod is higher than that for a lighter rod with the same geometry.

Towards Understanding Why the Thin Membrane Transducer Deforms:Surface Stress-Induced Buckling

This study is directed towards a comprehensive exploration on the deformation mechanism of the thin membrane transducer（TMT） caused by surface stress variation.We stress that the biomolecular interaction has changed the magnitude of the surface stress;and when the surface stress exceeds a critical value the TMT will buckle and deform.Based upon Gurtin＇s theory of surface elasticity and principle of finite deformation,we abstract the TMT as a nanobeam with two clamped ends,and the close-formed governing equation set is derived accordingly.A computer code via the shooting method is developed to solve the presented two-point boundary value problem.In succession,the nanobeam deflection and critical parameters for buckling are quantitatively discussed.This investigation lays the theoretical foundation of TMTs;and it is also beneficial to gain deep insight into characterizing mechanical properties of nanomaterials and engineering nano-devices.

Thermal Buckling Analysis of Size-Dependent FG Nanobeams Based on the Third-Order Shear Deformation Beam Theory

In this paper,the thermal effects on the buckling of functionally graded（FG） nanobeams subjected to various types of thermal loading including uniform,linear and non-linear temperature changes are investigated based on the nonlocal third-order shear deformation beam theory.The material properties of FG nanobeam are supposed to vary gradually along the thickness direction according to the power-law form.The governing equations are derived through Hamilton＇s principle and solved analytically.Comparison examples are performed to verify the present results.Obtained results are presented for thermal buckling analysis of FG nanobeams such as the effects of the power-law index,nonlocal parameter,slenderness ratio and thermal loading in detail.