Abstract
A piecewise continuous eigenfunction procedure is developed to handle the two and three dimensional stress fields of rectangular anisotropic laminated slabs. In particular, each lamina of the slab is considered to be modelled by exact anisotropic elasticity theory such that perfect bonding between adjacent laminae is assumed. Since the eigenfunction basis arising from the development is complete but nonorthogonal, a piecewise weighted reorthogonalization procedure or alternatively a multiply connected version of the Gram Schmidt process is employed in solving the eigenfunction expansion. In order to obtain the completely general boundary value solution, complex series and adjoint differential forms are also employed to handle inhomogeneities in the governing DEQ. Several numerical experiments are included to reveal the capabilities of the solution procedure developed as well as the potential local importance of material anisotropy.
Zusammenfassung
Ein Verfahren mit der stückweisekontinuierlichen Eigenfunktion hat sich entweckelt, die zwei und drei dimensionale Druckfelden der rechteckigen unisotropeblättrigen Schlämme anzufassn. Im besondern, jedes Plätchen vom Schlamm ist, als modelliert nach der genauen unisotropeelastischen Theorie, angesehen; derartig ist die unlösbare Verbindung zwischen anliegenden Plätchen angenommen. Weil die hervorkommende Eigenfunktionsbasis der Entwicklung vollständig ist, obwohl unorthogonal; ein Verfahren der stückweisebedeutunggegebenen Wiederorthogonalisation oder ausschließendlich, vielfachverbundene Version des Gram-Schmidt-Verfahrens ist verwendet, die Ausdehnung der Eigenfunktion aufzulösen. Für vollständige allgemeine Begrenzungwertlösung zu erreichen, sind auch die komplexe Serie und adjungierte Differentialformen gebraucht worden. Ungleichartigkeiten in der leitenden Differentialgleichung anzufassen. Viele numerische Experimenten sind eingeschloßen, die Fähigkeiten des sich entwickelten Lösungverfahrens aufzudecken; ebenso die potentielle lokale Wichtigkeit der Stoffunisotropie.
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Padovan, J. Piecewise continuous eigenfunction solutions for laminated slabs. J Elasticity 7, 337–352 (1977). https://doi.org/10.1007/BF00041727
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DOI: https://doi.org/10.1007/BF00041727