p-Version axisymmetric and three-dimensional curved shell elements for linear and nonlinear steady state heat conduction with isotropic, generally orthotropic and laminated composite material behavior
Complete hierarchical p-version axisymmetic and three dimensional curved shell finite elements are developed for isotropic, generally orthotropic and laminated material behavior for linear and nonlinear steady state heat conduction. The weak formulation is constructed for the axisymmetric and three dimensional cartesian coordinate partial differential equations for linear and nonlinear steady state heat conduction with anisotropic materials, and the quadratic functional is constructed for the linear case. The nonlinearities caused by the temperature dependent material properties as well as those caused by nonlinear boundary conditions are considered. The element geometries are defined by nodes located on the middle surface and nodal thickness vectors. The element temperature approximations are established by first constructing one dimensional hierachical Lagrangian approximation functions and nodal variable operators in each of the element directions and then taking their tensor product. The approximation functions and nodal variables are hierarchical. That is the temperature approximation corresponding to the polynomial order of (p + 1). The formulation ensures C[sup o] continuity. The element formulation is based on the minimization of the quadratic functional for the linear case, and Galerkin's method in the nonlinear case. Newton-Raphson's method is used to solve the system of nonlinear simulation s equations. Due to the hierarchical nature of the approximation, the element matrixes and load vectors are also hierarchical. Numerical examples are presented to show the validity, accuracy, advantages, applications, and limitations of the formulations.
- Research Organization:
- Kansas Univ., Kansas City, KS (United States)
- OSTI ID:
- 7070876
- Country of Publication:
- United States
- Language:
- English
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