An empirical formula to assess ultimate strength of initially deflected plate: Part 1 = propose the general shape and application to longitudinal compression

This study proposes a simplified empirical formulation to predict the ultimate strength of the initially deflected plate subjected to longitudinal compression. The empirical formulation's applicability and accuracy were verified by comparing the nonlinear finite element method (NLFEM). In total, 700 cases of initially deflected plate scenarios by assuming the buckling mode shape were adopted as the input data. For the simplification of the plate design process, a general shape of the empirical formula is proposed based on input data. A reliable technical solution is obtained with good agreements (R² = 0.98 to 0.99) compared to NLFEM. The advantage of the proposed outcome is documented by comparing the previous study. The obtained result could be beneficial for the structural design of the initially deflected plate in predicting its ultimate strength performance under longitudinal compression.