Carl H. Popelar

On the use of the complementary energy in the solution of buckling problems

Abstract A systematic derivation of the expression for the complementary energy in elastic buckling problems is presented. Compatibility is identified with variation with respect to the stress components, and the resulting eigenvalue problem is shown to be equivalent to, and sometimes more convenient than, the corresponding formulation in terms of the potential energy. Similarly, approximate techniques may lead to better as well as simpler estimates, whose upper bound property can, however, be assured only through appropriate safeguards. The method is applied in some detail to buckling of columns of arbitrary boundary conditions and axial force distribution. Another example is the problem of lateral beam buckling, with the effect of warping restraint included. In both cases (and presumably in many others) the complementary energy formulation is of lower order than the conventional potential energy formulation, and it is clear that the same simplification should also apply to finite elements or other discrete formats. The method is restricted to the (technically significant) case of a linear prebuckling state.

An evaluation of a free volume representation for viscoelastic properties

Abstract Creep data for two different polyethylenes which were not amenable to master curve formation have been adjusted using a simple free volume model to produce master curves characterizing creep at the limit of zero stress. The validity of these master curves has been checked against results from relaxation tests which are available for the same two materials.

Optimal Design of Structures Against Buckling: A Complementary Energy Approach

ABSTRACT The complementary energy approach is used to establish the basic principles in terms of generalized stress components for the optimum design of elastic structures against buckling. The necessary condition of optlmality is derived and its sufficiency is established for those structures whose compliance densities are convex and which are statically determinate. By way of illustration, the development is used to rederive the governing equations for the optimal design of a column against lateral buckling. The formulation is further applied to obtain optimum design of thin-walled beams against lateral-torsional buckling.

Optimal Design of Beams against Buckling: A Potential Energy Approach

Abstract A rather general development of the optimum design of structures against buckling is extended to include a broader class of structures and loadings. The development is specialized to the problem of optimal design of thin-walled beams against lateral buckling. The optimum design for simply supported, cantilever, and fixed-fixed rectangular beams in pure bending is found to be a uniform one. For simply supported rectangular beams of variable height the savings in weight compared to a uniform beam is insignificant. Significant savings can be realized for a constrained design of a class of I-beams of variable depth.

Creep crack growth in joints of a thermoplastic

An investigation of creep crack growth in butt heat fusion joints in a high density polyethylene (HDPE) is performed to quantify their life expectancy. Three point bend specimens containing a centrally located notched joint are used in creep crack growth tests at ambient and elevated temperatures. A quasi-nonlinear viscoelastic fracture mechanics model is used to deduce the crack growth histories from the measured load-point displacement histories. The initiation time for crack growth and the rate of crack growth are correlated with the stress intensity factor for combinations of initial crack lengths, applied loads and test temperatures. The elevated temperature data are shifted bidirectionally, utilizing shift functions derived from stress relaxation tests, to develop master curves for the initiation time and rate of crack growth. These master curves are used to predict the life of a girth joint containing an initial circumferential surface crack extending through 10 percent of the thickness of a pressurized pipe.

Dynamic stability of the flexural vibrations of a thin-walled beam

Abstract The stability of the free transverse vibrations of a simply supported, thin-walled elastic beam with double axes of symmetry is investigated for arbitrary initial velocity distributions. The lateral-torsional modes may be parametrically excited through the interaction of the pulsating flexural moment and the rotation of the cross section of the beam about the longitudinal axis and the vertical axis of symmetry. A criterion is presented to predict this excitation. A numerical example for a particular transverse flexural mode of vibration indicates that the critical initial velocity for lateral-torsional parametric excitation may be relatively small.

Theory of stability of an elastic cosserat surface

Abstract The theory of elastic stability of a Cosserat surface subjected to conservative, nongyroscopic surface and edge loading is presented. The equations of neutral equilibrium and a study of stability at the critical load is included. For the special case in which the deformation is such that the director may be identified with the unit normal to the surface, the results are shown to reduce to the generally accepted theory of stability of thin shells within the Kirchoff-Love hypothesis.

A fracture mechanics methodology for slow crack growth in thin polyimide films

A fracture mechanics methodology for assessing the influence of stress and defect size on the structural integrity and life expectancy of thin polyimide films is presented. The approach is a synergistic one that combines fracture mechanics analyses and experiments to quantify slow crack in the films. A viscoelastic fracture model is used to deduce the crack growth history from load-point displacement records measured during long-term fracture tests of the films. The rate of crack growth is found to depend very strongly upon the crack driving force as measured by the stress intensity factor. Hence, small changes in the stress intensity factor can produce dramatic changes in the crack growth rate in the materials investigated.<<ETX>>