Object composition offers significant advantages over class inheritance to develop a flexible software architecture for finite-element analysis. Using this approach, separate classes encapsulate fundamental finite-element algorithms and interoperate to form and solve the governing nonlinear equations. Communication between objects in the analysis composition is established using software design patterns. Root-finding algorithms, time integration methods, constraint handlers, linear equation solvers, and degree of freedom numberers are implemented as interchangeable components using the Strategy pattern. The Bridge and Factory Method patterns allow objects of the finite-element model to vary independently from objects that implement the numerical solution procedures. The Adapter and Iterator patterns permit equations to be assembled entirely through abstract interfaces that do not expose either the storage of objects in the analysis model or the computational details of the time integration method. Sequenc...

A new plastic hinge integration method overcomes the problems with nonobjective response caused by strain-softening behavior in force-based beam–column finite elements. The integration method uses the common concept of a plastic hinge length in a numerically consistent manner. The method, derived from the Gauss–Radau quadrature rule, integrates deformations over specified plastic hinge lengths at the ends of the beam–column element, and it has the desirable property that it reduces to the exact solution for linear problems. Numerical examples show the effect of plastic hinge integration on the response of force-based beam–column elements for both strain-hardening and strain-softening section behavior in the plastic hinge regions. The incorporation of a plastic hinge length in the element integration method ensures objective element and section response, which is important for strain-softening behavior in reinforced concrete structures. Plastic rotations are defined in a consistent manner and clearly relat...

An accelerated Newton algorithm based on Krylov subspaces is applied to solving nonlinear equations of structural equilibrium. The algorithm uses a low-rank least-squares analysis to advance the search for equilibrium at the degrees of freedom (DOFs) where the largest changes in structural state occur; then it corrects for smaller changes at the remaining DOFs using a modified Newton computation. The algorithm is suited to simulating the dynamic progressive collapse analysis of frames where yielding and local collapse mechanisms form at a small number of DOFs while the state of the remaining structural components is relatively linear. In addition, the algorithm is able to resolve erroneous search directions that arise from approximation errors in the tangent stiffness matrix. Numerical examples indicate that the Krylov subspace algorithm has a larger radius of convergence and requires fewer matrix factorizations than Newton-Raphson in the dynamic progressive collapse simulation of reinforced concrete and ...

A probabilistic framework is presented for the development of physics and simulation-based parametrized tsunami fragility functions for structures accounting for structural member failures. The proposed framework is general and accounts for material and geometric sources of uncertainty and makes use of nonlinear finite-element structural models and the first-order second-moment (FOSM) reliability method. The application of the framework is illustrated with the development of parametrized fragility functions for an example reinforced concrete moment frame building designed to recent United States codes. Results indicate that explicit consideration of structural member failures is of paramount importance because the fragility functions based on global failure criteria that do not account for member failures tend to overpredict damage state capacities. Among the several sources of uncertainty considered, breakaway openings in the building are the dominant contributor to the uncertainty in the structural capacity. In addition, the estimation efficiency of several scalar and vector-valued intensity measures as predictors of structural damage is evaluated using the logistic regression method. The intensity measures considered consist of inundation depth, flow velocity, specific momentum flux, kinematic moment of specific momentum flux, and their interactions. The estimation efficiency of vector-valued intensity measures is found to be higher than that of scalar intensity measures. Among the scalar intensity measures analyzed, those that combine information of inundation depth and flow velocity are identified to be the most efficient predictors of structural damage, and therefore are considered to be the preferred measures to characterize the intensity of tsunami hazards for practical applications.

A framework for simulating the material and geometric nonlinear response of frame members is developed from the equations of beam mechanics. The implementation of a beam-column finite element is reduced to the state determination procedure for a basic system that displaces and rotates with the element. An abstraction for geometric nonlinearity represents the kinematic and equilibrium transformations between the basic and global reference systems, while an abstraction for force-deformation response represents material nonlinearity for the basic system. Separate objects encapsulate material stress-strain behavior and cross-sectional integration in order to increase the modeling flexibility for computing the response of fiber-discretized cross sections. Multiple forms of distributed plasticity in beam-column elements are incorporated in the framework through objects that encapsulate one-dimensional quadrature rules. Software design patterns are utilized to create complex beam-column simulation models by comp...