A Finite Element Analysis of Optimal Variable Thickness Sheets

Joakim S Petersson

A Finite Element Analysis of Optimal Variable Thickness Sheets

Joakim S Petersson

Research output: Book/Report › Report › peer-review

Abstract

A quasimixed Finite Element (FE) method for maximum stiffness of variablethickness sheets is analysed. The displacement is approximated with ninenode Lagrange quadrilateral elements and the thickness is approximated aselementwise constant. One is guaranteed that the FE displacement solutionswill converge, but in an example it is shown that, in general,one cannot expect any subsequence of the FE thickness solutions to converge.However, under a regularity and biaxiality assumptionon the optimal stress field, uniqueness of the optimal thickness function aswell as convergence of FE thickness solutions are proven.

Original language	English

Number of pages	21
Publication status	Published - 1996

Cite this

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title = "A Finite Element Analysis of Optimal Variable Thickness Sheets",

abstract = "A quasimixed Finite Element (FE) method for maximum stiffness of variablethickness sheets is analysed. The displacement is approximated with ninenode Lagrange quadrilateral elements and the thickness is approximated aselementwise constant. One is guaranteed that the FE displacement solutionswill converge, but in an example it is shown that, in general,one cannot expect any subsequence of the FE thickness solutions to converge.However, under a regularity and biaxiality assumptionon the optimal stress field, uniqueness of the optimal thickness function aswell as convergence of FE thickness solutions are proven.",

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AB - A quasimixed Finite Element (FE) method for maximum stiffness of variablethickness sheets is analysed. The displacement is approximated with ninenode Lagrange quadrilateral elements and the thickness is approximated aselementwise constant. One is guaranteed that the FE displacement solutionswill converge, but in an example it is shown that, in general,one cannot expect any subsequence of the FE thickness solutions to converge.However, under a regularity and biaxiality assumptionon the optimal stress field, uniqueness of the optimal thickness function aswell as convergence of FE thickness solutions are proven.

M3 - Report

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