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key words: Finite element, mesh refinement, hierarchical, adaptive approximation, object-oriented design SUMMARY A new approach to the construction of adaptive approximations on finite element meshes and also in more general settings, including approximations on subdivision surfaces, had been recently proposed by Krysl, Grinspun, and Schröder. This paper outlines how the general refinement algorithms may be specialized to some common finite element discretizations in two and three dimensions, discusses the design of nested meshes, and delves into the algorithmic, design, and implementation issues in an object oriented software framework

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A constitutive theory is proposed for FRP laminated composite materials that is designed to account for both temperature and strain rate dependent response, such as would occur during, and after, exposure to the elevated temperatures due to fire. The theory is physically based, and in particular, is based on a kinematical framework fixed on the fabric laminates; full accounting of laminate reorientation and anisotropic response is thus achieved. The theory is numerically implemented and FEM analysis of compressive deformation of a sandwich panel, given as an example, demonstrates how common material failure modes such as kinking are naturally included in the theory and in analyses using the theory. The theory accounts for finite strains and thus extent of deformation is arbitrary. The theory and its numerical implementation are designed specifically to perform numerical analysis of structural response of FRP structures subject to fire degradation.