Theory Manual

This manual describes the formulations used internally by FrontISTR. Rather than serving as a general textbook introduction to the finite element method, it is limited to the specific formulations and algorithms that support FrontISTR analysis functions.

For an overview of each function and guidance on selecting among them, see the Function Reference. For input-file syntax, see the Keyword Reference.

Chapter Structure

• Linear Elastic Static Analysis (Introduction/Appendix) — an introductory summary that presents, in a single self-contained chapter, the derivation from the weak form to the global equation \(KU=F\) under the assumptions of infinitesimal deformation and linear elasticity
• Notation — conventions for tensor notation and Voigt notation
• Governing Equations of Fields — fundamentals of continuum mechanics (motion, deformation, and strain / stress and conservation laws / principle of virtual work), and the heat conduction equation
• Constitutive Laws — linear elasticity, hyperelasticity, elastoplasticity, viscoelasticity, creep, and thermal properties
• Discretization — weak forms and the finite element method, element formulations
• Solution Algorithms — nonlinear static analysis (incremental analysis framework / Total Lagrange / Updated Lagrange / Newton-Raphson method and convergence criteria), dynamic analysis, modal analysis, frequency response analysis, and transient heat conduction analysis
• Contact — formulation of contact problems
• Linear Solvers — mathematical principles of iterative and direct methods
• Parallel Computing — parallel finite element method based on domain decomposition
• References