Issue 50

K. Meftah et alii, Frattura ed Integrità Strutturale, 50 (2019) 276-285; DOI: 10.3221/IGF-ESIS.50.23 284 Clamped square plate A clamped square plate subjected to uniform load is analyzed. Fig. 7 shows the load-deflection curve with respect to maximum deflection with ( h = 0.01). The present 4-node element Q4  results are compared with those of Hétérosis finite element reported by Owen and Hinton [1]. From this figure, it is observed that the results provided by the present four- node Q4  element are in a good agreement with those of the converged results of the 9-node Hétérosis element given in [1]. The progression of the yield regions at different levels of loading is summarized in Fig. 8. In this case, the first yielding of the plate occurs at the middle of the four edges, and the plastic regions extend along these edges until the center of the plate yields. 0 5 10 15 20 25 0 10 20 30 40 50 60 Elément Hétérosis Elément Q4Gamma ² . . 0 LM DW 0 ² . M Lq Hétérosis element Q4G ele ent Figure 7 : Load-deflection curves for clamped square plate ( h = 0.01). 0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1 0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1 1.74E5+ 1.59E5 to 1.74E5 1.43E5 to 1.59E5 1.27E5 to 1.43E5 1.11E5 to 1.27E5 9.52E4 to 1.11E5 7.93E4 to 9.52E4 6.34E4 to 7.93E4 4.76E4 to 6.34E4 3.17E4 to 4.76E4 1.59E4 to 3.17E4 0.00E0 to 1.59E4 Figure 8 : Progression of Yield regions for clamped square plate ( h = 0.01). C ONCLUSIONS n this work, a finite element method for analyzing the problem of elasto-plastic bending of a square plate is presented. The previously proposed four-node Q4  element with transverse energy of shearing for thick bending plates is extended to account for nonlinear elasto-plastic problems. The adopted constitutive model is the classical associative Von-Mises plasticity model where the modified Newton-Raphson scheme has been implemented for solving the nonlinear numerical system. To perform numerical tests, various examples within the nonlinear context are used to assess the accuracy against currently existing well-performed elements. The present element shows reliability and I