Finite element method

Abstract

This course on the Finite Element Method (FEM) is primarily designed for third-year undergraduate students enrolled in the Naval Engineering program, specializing in shipbuilding and naval architecture under the LMD system. The handout aims to facilitate students’ understanding the use of FEM to solve problems related to strength of materials filed . The course is organized into three comprehensive chapters: The first chapter offers a broad overview of FEM, covering its objectives, fundamental concepts, advantages, and areas of application. It also introduces the discretization approach used in finite element calculations, explaining how continuous domains are subdivided into finite elements for analysis. The second chapter focuses on deriving the stiffness matrix for a bar element. It extends this study to truss structures, illustrating how these elements combine to form complex frameworks. Several solved problems are included to reinforce the theoretical concepts. Additionally, three classical methods for calculating deflection and rotation are presented: The third chapter develops the application of FEM to beam bending problems. It begins with the construction of the stiffness matrix for a beam element and builds upon the theoretical foundation to analyze bending behavior. This chapter includes key questions, worked examples, and straightforward applications designed to deepen students’ comprehension and practical skills. Throughout the document, emphasis is placed on linking theory with practice, enabling students to confidently apply FEM techniques to real-world naval engineering problems