Parsons-TJ; GangaRao-HV; Peterson-WC
Comput Struct 1985 Sep-Oct; 20(5):877-883
Methods of analyzing plate behavior via a macro element approach were presented. Deflected shapes of macro elements of rectangular shapes were obtained by a shape function satisfying the four boundary conditions and the biharmonic equation. The shape functions were a sum of sinusoidal and polynomial terms with undetermined coefficients. The elements that satisfied moment and shear conditions were assembled by using compatibility equations for deflection and slope. Equilibrium of forces and moments for all lines along the common edges of macro elements were attained. Convergence studies were performed for three bounded domains and the results compared to solutions obtained from classical and finite element methods; the deflection converged to within two percent. The convergence of the macro approach was checked by progressively increasing the number of harmonics; excellent results were obtained within the first three harmonics. The authors conclude that there are several advantages to the macro approach: it deals with more complex shape functions with less input effort than the classical finite element methods; highly accurate and reliable macro elements are available; the deflection and moment values at any point in the domain and on the boundary can be determined; and compatibility of deflection, slope, and moment can be obtained with the aid of a continuous function along the common edge.
Analytical-models; Structural-analysis; Analytical-methods; Mathematical-models; Engineering; Analytical-processes
Computers & Structures