CLOSED-FORM SOLUTION OF A METAL PLATE WITH A CENTRAL CRACK UNDER TENSION

Abstract

Accurate prediction of stress and displacement in plates with central cracks is vital for engineering design safety. However, the impact of finite plate size on stress and displacement distribution is an important factor that has not been fully addressed in previous studies, highlighting the need for further investigation. Thus, this study presents a closed-form elastic solution for a rectangular plate with a central crack under tension load. The solution uses complex polynomial functions satisfying equilibrium equations and boundary conditions. Numerical finite element models verify the analytical solution's accuracy for plates with varying crack lengths. The presented closed-form solution accounts for the impact of finite plate size on stress and displacement distribution accurately. Developing closed-form solutions for structural mechanics problems enables engineers to optimize designs for safety, efficiency, and cost-effectiveness more accurately.