An approximate solution to the finite deformation of an elastic rectangular plate under static and dynamic transverse loadings

摘要

In the field of structure safety, the blast resistance of glazing is increasingly important. This problem could be simplified as a finite deformation rectangular plate under dynamic loading, whose traditional solution is still insufficient in accuracy. Based on von K & acute;arm & acute;an equations, this paper aims to offer an efficient and acceptable approximate solution. Two basic assumptions are adopted: a) the strain distribution along the principle direction of the mid-plane is uniform; b) the in-plane shear stress is ignored. The membrane stresses are expressed by the deflection of the plate, and then the von K & acute;arm & acute;an equations are de-coupled.Both static and dynamic solutions of current model are verified by finite element simulations, popularly used standards and experiment data. For the simply supported plates, the deflection and stresses predicted by current model are quite accurate. For the fully clamped plates, the deflection predicted is good, but the stress given has a big error, due to the lack of high order deflection modes. Besides, in predicting stresses, the effect of higher orders of deflection modes is discussed. It is confirmed that the accuracy of current approximate solution is sufficient to determine the maximum 1st principle stress of plates, and to give an efficient failure criterion of glazing under blast loading.