Harry E. Williams

ASYMPTOTIC ANALYSIS OF THE THERMAL STRESSES IN A TWO-LAYER COMPOSITE WITH AN ADHESIVE LAYER

The room temperature stresses induced in a composite structure after cool-down from a high temperature are studied within the framework of linear thermoelasticiry. The equations governing a one-dim...

Stress and Displacement Estimates for Arches

This paper presents analytical estimates of the behavior exhibited by curved, archlike structures under radially directed and gravitational line loads. The behavior is shown to range from elementary beam bending at one end to a state of pure compression at the other, and its behavior can be tracked by an arch rise parameter that is a function of the arch’s semivertex angle, radius and thickness. The principal results are useful estimates of the dependence of the major displacements and stress resultants on the arch rise parameter. The results also offer some insight into the assumptions underlying Robert Maillart’s arch designs.

On the equations of motion of thin rings

The equations of motion governing small, elastic displacements, including warping effects, are derived by using Hamiltons Theorem. The stress-resultant displacement equations are identified through the natural boundary conditions. It is shown that the governing equations obtained are consistent with those obtained by using momentum principles. Of particular importance is the appearance of a “twist” equation of motion relating the twisting moment and the St. Venant torsion moment. Numerical results are presented for the frequencies and mode shapes of both complete rings and ring segments.

On the in-plane motion of thin, rotating ring segments

Abstract The equations governing the motion of a thin, circular ring, rotating about its polar axis, are derived under the restriction that plane sections remain plane and normal to the deformed centroidal curve. Simplified equations are then obtained for displacements that are small in comparison to the ring thickness, and for time scales that are comparable with the period of flexural vibration. Solutions are obtained for free vibration, and numerical results presented for the frequencies and mode shapes of a semi-circular ring fixed at both ends. The solution for forced motion is shown to be expressible as a modal expansion in these characteristic functions.

THERMAL STRESSES IN BONDED SOLAR CELLS-THE EFFECT OF THE ADHESIVE LAYER

A two-dimensional, rectangular model of a proposed solar cell structure is analyzed as two plate elements bonded with an elastic continuum. The governing equations are formulated using the principle of minimum potential energy, with displacement components that vary linearly through the thickness of the adhesive layer. An approximate solution is constructed for a particular class of material properties and is characterized by a boundary layer near the unloaded edge. Both interface stress components achieve their largest values at the edge, and the maximum shear stress is independent of the Youngs Modulus of the substrate.

Exploring physical intuition in elementary pressure vessels

It is shown that displacement calculations for two classical ‘chestnuts’ – thick cylinders and spheres under internal and external pressures – present results that are not easily anticipated. Thus, such analyses provide an interesting opportunity for students (and teachers) taking elementary and advanced courses in the strength of materials to explore and perhaps enhance their physical intuition.

A Note on the Use of the Instant Center as a Reference Point for Angular Momentum Theorems

The use of the instant center as a reference point in angular momentum theorems has the advantage that unknown contact forces do not appear in the equations of motion. However, care must be taken to distinguish the point as being on the body or the space centrode.

On free vibration of thin, cylindrical shells with large circumferential wavenumber: Rayleigh's solution

The method of matched asymptotic expansions is used to obtain the natural frequencies and mode shapes for thin (ha → 0) cylindrical shells corresponding to large circumferential wavenumbers n, where n = O((ah)12). The deformation is nearly inextensional: the frequency results are similar to Rayleighs result and are independent of end fixity through O(1n2) compared to unity.

On the boundary conditions for the membrane equations of thin, cylindrical shells and resulting natural frequencies

Abstract The method of matched asymptotic expansions is applied to the classical equations of motion for thin, cylindrical shells to extract the correct boundary conditions to apply to the membrane equations. Numerical results for natural frequencies are obtained for fixed-fixed and fixed-free ends, and are shown to be valid for small circumferential wavenumbers.

“NEALE PLATE“ EQUATIONS AND APPLICATIONS TO BUCKLING OF RECTANGULAR PLATES

Abstract The field equations associated with Neales variational theorem are developed and applied to the problem of buckling and postbuckling of heated, constrained flat plates. The resulting equations are a generalization of Karmans equations in rate form, having a constitutive equation in which the strain/curvature rates are a linear combination of the stress resultant rates. In the immediate neighborhood of a critical point, the theory predicts a substantial reduction of the buckling temperature due to plasticity effects. Further, for long strips, the force stress resultant in the short direction appears to decrease in absolute value after buckling, while the force stress resultant in the long direction appears to increase in absolute value.