👉 Expansys, a leading structural and thermal analysis software, utilizes advanced mathematical models to simulate complex engineering problems. At its core, the software employs finite element analysis (FEA), a numerical method that breaks down complex structures into smaller, manageable elements to solve differential equations that describe physical phenomena like stress, strain, heat transfer, and fluid flow. These equations are derived from fundamental principles of physics, such as Newton's laws of motion and the conservation of mass-energy. Expansys employs a variety of mathematical techniques, including linear algebra for solving large systems of equations, partial differential equations (PDEs) to model spatial variations in physical properties, and numerical integration methods to approximate solutions at discrete points within the elements. The software also incorporates advanced constitutive models that describe material behavior under different loading conditions, ensuring accurate predictions of structural response and thermal performance. By combining these mathematical tools with high-performance computing, Expansys enables engineers to analyze and optimize designs for safety, efficiency, and performance in a wide range of applications, from civil infrastructure to aerospace and automotive industries.