Publicación: A FINITE ELEMENT METHOD FOR THE BUCKLING PROBLEM OF SIMPLY SUPPORTED KIRCHHOFF PLATES
Fecha
2015
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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Resumen
THE AIM OF THIS PAPER IS TO DEVELOP A FINITE ELEMENT METHOD TO APPROXIMATE THE BUCKLING PROBLEM OF SIMPLY SUPPORTED KIRCHHOFF PLATES SUBJECTED TO GENERAL PLANE STRESS TENSOR. WE INTRODUCE AN AUXILIARY VARIABLE W:=ALFA U (WITH U REPRESENTING THE DISPLACEMENT OF THE PLATE) TO WRITE A VARIATIONAL FORMULATION OF THE SPECTRAL PROBLEM. WE PROPOSE A CONFORMING DISCRETIZATION OF THE PROBLEM, WHERE THE UNKNOWNS ARE APPROXIMATED BY PIECEWISE LINEAR AND CONTINUOUS FINITE ELEMENTS. WE SHOW THAT THE RESULTING SCHEME PROVIDES A CORRECT APPROXIMATION OF THE SPECTRUM AND PROVE OPTIMAL ORDER ERROR ESTIMATES FOR THE EIGENFUNCTIONS AND A DOUBLE ORDER FOR THE EIGENVALUES. FINALLY, WE PRESENT SOME NUMERICAL EXPERIMENTS SUPPORTING OUR THEORETICAL RESULTS.
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SPECTRAL ANALYSIS, KIRCHHOFF PLATES, FINITE ELEMENTS, ERROR ESTIMATES, BUCKLING PROBLEM
