Nonlinear Kinematic Relations Research Articles

Stability and Strength of Rigid and Semirigid Plane Frameworks

A computational technique for incorporating stability and strength into the analysis of plane frameworks is presented. The procedure for computing critical and/or collapse loads and for identifying the corresponding failure mode is outlined. The analysis is based on nonlinear kinematic relations and linearly elastic material behavior except at the plastic hinges—concentrated plasticity. The connections can be treated either as rigid or as flexible. The supports, in general, contain rotational restraints. The developed solution methodology is applicable to all multistory‐multibay orthogonal frames. The examples analyzed in the paper include: (1) A single‐story‐two‐bay frame with rigid joint connections; (2) a single‐story‐three‐bay frame with flexible joint connections; (3) a two‐story‐single‐bay frame with both rigid and flexible joint connections; and (4) a three‐story‐two‐bay frame with rigid joint connections. In all cases the loading consists of a symmetric distribution of concentrated loads on the beams, applied at the midspan positions and at or near the beam‐to‐column joints. The effect of several geometric and structural parameters is assessed.

Thermo-elastoviscoplastic snapthrough behavior of cylindrical panels

The thermo-elastoviscoplastic snapthrough behavior of simply supported cylindrical panels is investigated. The analysis is based on nonlinear kinematic relations and nonlinear rate-dependent unified constitutive equations which include both Bodner-Partom's and Walker's material models. A finite element approach is employed to predict the inelastic buckling behavior. Numerical examples are given to demonstrate the effects of several parameters which include the temperature, thickness and flatness of the panel. Comparisons of buckling responses betweeen Bodner-Partom's model and Walker's model are given. The creep buckling behavior, as an example of time-dependent inelastic deformation, is also presented.

Elasto-plastic analysis of gabled frames with nonprismatic geometries

A nonlinear elasto-plastic instability analysis of flexibly connected and supported gabled frames with nonprismatic geometry is presented. The analysis incorporates stability and strength. The procedure is based on nonlinear kinematic relations and linearly elastic behavior, except at the plastic regions (concentrated plasticity). The nonlinear flexible connections are represented by polynomial models. The effects of several parameters are considered in order to enhance our understanding of frame behavior. These include the effects of nonprismatic geometry, of rotational restraints at the supports, of rise to span ratio, of slenderness ratio and of joint flexible connection. Some representative results from the chosen examples are also presented.

Elastoviscoplastic snap-through behavior of shallow arches subjected to thermomechanical loads

The problem of snap-through buckling of clamped shallow arches under thermomechanical loads is investigated. The analysis is based on nonlinear kinematic relations and nonlinear rate-dependent unified constitutive equations. A finite element approach is employed to predict the, in general, inelastic buckling behavior. The construction material is alloy B1900+Hf, which is commonly utilized in high-temperature environments. The effect of several parameters is assessed. These parameters include the rise parameter and temperature. Comparison between elastic and elastoviscoplastic responses is also presented.

Stability and Collapse of Semirigidly Connected Portal Frames

A numerical procedure for the nonlinear elastic‐plastic instability analysis and collapse of semirigidly connected portal frames, with elastic rotational restraints at the supports, is presented. The procedure is based on nonlinear kinematic relations and linearly elastic material behavior except at the plastic regions (concentrated plasticity). The nonlinear flexible connections are represented by polynomial models. A computational technique for incorporating the stability and strength into the analysis is described in detail. It is found that several important parameters affect the failure modes and consequently the critical loads. These parameters are the slenderness ratio, support restraints, type of connections, and the loading conditions. It is also demonstrated that the connection flexibility has considerable effect on the critical load and the deformation. It is further concluded that for design application the assumption of linear (instead of nolinear, polynomial) connection behavior is adequate for portal frames only if the loading conditions do not produce a significant amount of bending moment at the joints.

Instability and collapse of flexibly-connected gabled frames

A nonlinear elasto-plastic instability analysis of flexibly connected and supported gabled frames with uniform and nonuniform geometry is presented. The analysis incorporates stability and strength. The procedure is based on nonlinear kinematic relations and linearly elastic material behavior except at the plastic regions (concentrated plasticity). The nonlinear flexible connections are represented by polynomial models. Thus, various types of response can be predicted. Through the chosen examples, the following types of response have been observed: elastic bifurcation instability, elastic limit point instability, elasto-plastic limit point instability and plastic collapse. The effect of several parameters is assessed in order to enhance our understanding of frame behavior. These include the effects of nonuniform geometry, of rotational restraints at the supports, of rise to span ratio, of beam to column stiffness ratio, of load eccentricity and of joint flexible connections.

Stability of imperfect laminated cylinders - A comparison between theory and experiment

A comparison between analytical results (critical loads) and experimental results (buckling loads) is presented for imperfect, laminated, circular, cylindrical, thin shells. The loading consists of uniform axial compression and torsion, applied individually and in combination (load cases for which results are published in the open literature). The imperfection shape and amplitude of the experimental results are explicitly given for some data and not for others. In the latter case, the comparison is qualitative. The theoretical results are obtained from a solution methodology that was developed and previously reported by the authors. It is based on nonlinear kinematic relations, linearly elastic material behavior, and the usual lamination theory. The comparison serves as an experimental verification for the analytical solution scheme.

The effect of various parameters on the nonlinear sway-buckling of a three-bar frame

In this investigation the postbuckling response of an unbraced rectangular three-bar frame subjected to a vertical concentrated load at its joint is discussed on the basis of an energy (variational) approach and nonlinear kinematic relations. It is found that the sway-buckling mode of the perfect frame is associated with a symmetric unstable bifurcation point which degenerates into a limit point when small initial imperfections are present. The effects of loading eccentricity, slenderness ratio, moment of inertia and length ratios on the carrying load capacity of the frame are fully assessed.

Effect of shear deformation on post‐buckling behaviour of columns

AbstractThe post‐buckling behaviour of a cantilever column of variable moment of inertia with tip load is studied by means of a simple numerical iterative scheme. The governing equation of equilibrium is formulated using the axial and transverse displacement quantities, and applying linear constitutive and nonlinear kinematic relations. Numerical results obtained by numerical iterative procedure are presented in the form of curves showing the relation between non‐dimensional tip‐deflection and non‐dimensional load for different values of shear correction factors and taper ratios.

Buckling of Imperfect Stiffened Cylinders under Destabilizing Loads including Torsion

This paper deals with the buckling of imperfect, thin, circular, cylindric, stiffened shells under the application of destabilizing loads, including uniform axial compression, lateral pressure, and torsion. The analysis includes individual load application as well as the case of combined loads. The methodology presented is based on the smeared technique, the Yon Karman-Donnell nonlinear kinematic relations, linear constitutive relations, and it considers the most general shape of a geometric imperfection. Numerical results for various configurations are presented. From the limited cases considered, one may conclude that stiffened configurations are not as sensitive as unstiffened ones, when loaded in torsion.

Buckling Analysis of Geometrically Imperfect Stiffened Cylinders under Axial Compression

The buckling analysis of an imperfect, thin, circular, cylindrical, stiffened shell under uniform axial compression and for various end conditions is investigated. A methodology is presented for predicting critical conditions for such configurations. This methodology is based on the smeared technique and the von KarmanDonnell nonlinear kinematic relations in the presence of geometric imperfections. The computational procedure employs a Fourier series type of separated solution, and through the Galerkin procedure the field equations are reduced to a system of ordinary differential equations. These equations are solved by the finite-difference scheme. Numerical results for numerous stiffened and unstiffened configurations are presented.