A Computationally Time-Efficient Method for Implementing Pressure Load to FE Models with Lagrangian Elements

Abstract

A computationally time-efficient method is introduced to implement pressure load to a Finite element model. Hexahedron elements of the Lagrangian family with Gauss–Lobatto nodes and integration quadrature are utilized, where the integration points follow the same sequence as the nodes. This method calculates the equivalent nodal force due to pressure load using a single Hadamard multiplication. The arithmetic operations of this method are determined, which affirms its computational efficiency. Finally, the method is tested with finite element implementation and observed to increase the runtime ratio compared to the conventional method by over 20 times. This method can benefit the implementation of finite element models in fields where computational time is crucial, such as real-time and cyber–physical testbed implementation.

Keywords

• equivalent pressure load
• Lagrangian
• Gauss–Lobatto nodes
• computational time efficient
• real-time FEM