Geometric nonlinear analysis of structures is not a simple extension from its counterpart of linear analysis. In this article, some research works conducted primarily in the past two decades on the geometric nonlinear analysis of framed structures that are readily available to the authors, including, in particular, those conducted by the senior author and coworkers, will be briefly reviewed. To highlight the key features of geometric nonlinear analysis, each of the papers cited will be reviewed according to one or more of the following categories: a) analytical or semi-analytical works, b) formulation of incremental nonlinear theory, c) discrete vs connected element and procedure of assembly, d) joint equilibrium conditions in the deformed configuration, e) rigid body test for nonlinear finite elements, f) key phases in incremental-iterative analysis, g) force recovery procedure, h) strategy for incremental-iterative approaches, i) rigid body-qualified geometric stiffness matrix, j) formulation and simulation for curved beam problems, k) special considerations for truss structures, and l) other related considerations. Throughout this article, emphasis will be placed on the theories and procedures leading to solution of the load-deflection response of structures, which may involve multi-looping curves in the postbuckling range. In fact, a nonlinear analysis using incremental-iterative schemes need not be as complicated as we think. If due account can be taken of the rigid body behaviors at each stage, then the whole process of incremental-iterative analysis can be made simpler and more efficient. Even when the postbuckling behavior of structures is of concern, the use of an accurate elastic stiffness matrix plus a rigid-body-qualified geometric stiffness matrix can always yield satisfactory results. There are 122 references cited in this review article.
A strut-and-tie design methodology is presented for three-dimensional reinforced concrete structures. The unknown strut-andtie model is realized through the machinery of a refined evolutionary structural optimization method. Stiffness of struts and ties is computed from an evolved topology of a finite element model to solve statically indeterminate strut-and-tie problems. In addition, compressive strength for struts and nodal zones is evaluated using Ottosen's four-parameter strength criterion. Numerical examples are studied to demonstrate that the proposed design methodology is suitable for developing and analyzing three-dimensional strut-and-tie models for reinforced concrete structures.
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