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The bubble size distribution created by the expanding foam plays a key role in controlling the load-bearing and other mechanical properties of the manufactured structural foam part. A numerical method to study the bubble growth and predict the bubble size distribution in polymeric foams is presented. On the microscopic scale, a cell model has been used. A cell is a system composed of a hypothetical spherical gas bubble and an envelope of polymer with constant mass surrounding the bubble. On the macroscopic scale, the foam has been modeled as a compressible medium consisting of a number of cells growing in close proximity to each other. The coupled system of the bubble growth equations for a cell and the field equations for the polymeric fluid are solved numerically to predict the spatial bubble size distribution and the flow front movement during the expansion process. The influence of different dimensionless parameters on the growth of spatially distributed bubbles and on the relative reduction in the transient bulk foam density, under isothermal condition, has been predicted. The existence of an axial pressure gradient in the mold due to the spatial variation of bubble growth is demonstrated through numerical experiments.

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The dynamics of a large number of bubbles separated by distances of the order of their radii in highly viscous fluids with specific application to foams is investigated. The growth of bubbles is due to diffusion of gas from the fluid and the momentum transfer between the fluid and the bubbles. Equations governing the growth of a single bubble in a shell of fluid containing limited dissolved agas are coupled with the transport equations for the fluid under non‐isothermal conditions. The resulting set of equations are solved numerically for a system of bubbles growing along the axial direction in a mold. The results predict a bubble size distribution along the axial direction with large bubbles close to the melt front and smaller bubbles close to the gate, which results in a density distribution in the molded article. Experimental studies on structural foam under nonisothermal conditions are performed. The transient bulk foam density is measured by monitoring the melt front as the foam expands. The predicted values of the foam density are compared with the experimental results and the sources of error are discussed.

In this paper, the buckling analysis of laminated composite plates reinforced by single-walled carbon nanotubes (SWCNTs) is carried out using an analytical approach as well as the finite element method. The developed model is based on the classical laminated plate theory (CLPT) and the third-order shear deformation theory for moderately thick laminated plates. The critical buckling loads for the symmetrical layup are determined for different support edges. The Mori-Tanaka method is employed to calculate the effective elastic modulus of composites having aligned oriented straight nanotubes. The effect of the agglomeration of the randomly oriented straight nanotubes on the critical buckling load is also analyzed. The results of analytical solution are compared and verified with the FEM calculations The critical buckling loads obtained by the finite element and the analytical methods for different layup and boundary conditions are in good agreement with each other. In this article, the effects of the carbon nanotubes (CNTs) orientation angle, the edge conditions, and the aspect ratio on the critical buckling load are also demonstrated using both the analytical and finite element methods.

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The small-scale effect on the torsional buckling of a double-walled carbon nanotube (DWCNT) embedded on Winkler and Pasternak foundations is investigated in this study using the theory of nonlocal elasticity. The effects of the surrounding elastic medium, such as the spring constant of the Winkler type and the shear constant of the Pasternak type, as well as the van der Waals (vdW) forces between the inner and the outer nanotubes are taken into account. Finally, based on the theory of nonlocal elasticity and by employing the continuum models, an elastic double-shell model is presented for the nonlocal torsional buckling load of a DWCNT. It is seen from the results that the shear constant of the Pasternak type increases the nonlocal critical torsional buckling load, while the difference between the presence and the absence of the shear constant of the Pasternak type becomes large. It is shown that the nonlocal critical buckling load is lower than the local critical buckling load. Moreover, a simplified analysis is carried out to estimate the nonlocal critical torque for the torsional buckling of a DWCNT.