Software Patterns for Nonlinear Beam-Column Models

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 composition of basic building blocks. The modeling flexibility of the software design is demonstrated through the simulation of a reinforced concrete column.

[1]  Siu-Lai Chan,et al.  Elastoplastic and Large Deflection Analysis of Steel Frames by One Element per Member. I: One Hinge along Member , 2004 .

[2]  Melbourne Fernald Giberson,et al.  The response of nonlinear multi-story structures subjected to earthquake excitation , 1967 .

[3]  F. Filippou,et al.  Geometrically Nonlinear Flexibility-Based Frame Finite Element , 1998 .

[4]  Gregory R. Miller,et al.  An algorithmic framework for flexible finite element-based structural modeling , 1996 .

[5]  Marco Petrangeli,et al.  A FIBRE FINITE BEAM ELEMENT WITH SECTION SHEAR MODELLING FOR SEISMIC ANALYSIS OF RC STRUCTURES , 1998 .

[6]  Ricardo O. Foschi,et al.  Object-oriented finite element analysis , 1990 .

[7]  G. Powell,et al.  3D Beam‐Column Element with Generalized Plastic Hinges , 1986 .

[8]  T. Paulay,et al.  Seismic Design of Reinforced Concrete and Masonry Buildings , 1992 .

[9]  Thomas Zimmermann,et al.  Object-oriented finite element programming: I: Governing principles , 1992 .

[10]  K. Hjelmstad,et al.  Variational Basis of Nonlinear Flexibility Methods for Structural Analysis of Frames , 2005 .

[11]  Vitelmo V. Bertero,et al.  Earthquake Engineering: From Engineering Seismology To Performance-Based Engineering , 2020 .

[12]  Ivar Jacobson,et al.  The Unified Modeling Language User Guide , 1998, J. Database Manag..

[13]  Michael H. Scott,et al.  Plastic Hinge Integration Methods for Force-Based Beam¿Column Elements , 2006 .

[14]  Gregory L. Fenves,et al.  Software framework for distributed experimental–computational simulation of structural systems , 2006 .

[15]  H. Tanaka,et al.  Effect of lateral confining reinforcement on the ductile behaviour of reinforced concrete columns , 1990 .

[16]  Robert Ian Mackie.  Object oriented programming of the finite element method , 1992 .

[17]  D. Addessi,et al.  A regularized force‐based beam element with a damage–plastic section constitutive law , 2007 .

[18]  Graham C. Archer,et al.  A new object-oriented finite element analysis program architecture , 1999 .

[19]  Gregory L. Fenves.  Object-oriented programming for engineering software development , 2005, Engineering with Computers.

[20]  Gregory G. Deierlein,et al.  STRESS-RESULTANT PLASTICITY FOR FRAME STRUCTURES , 1998 .

[21]  R. Park,et al.  Flexural Members with Confined Concrete , 1971 .

[22]  Robert L. Taylor,et al.  A mixed finite element method for beam and frame problems , 2003 .

[23]  M. Menegotto.  Method of Analysis for Cyclically Loaded R. C. Plane Frames Including Changes in Geometry and Non-Elastic Behavior of Elements under Combined Normal Force and Bending , 1973 .

[24]  Gregory L. Fenves,et al.  Object-oriented finite element programming: frameworks for analysis, algorithms and parallel computing , 1997 .

[25]  Michael H. Scott,et al.  Software frameworks for the computational simulation of structural systems , 2004 .

[26]  R. M. Souza.  Force-based Finite Element for Large Displacement Inelastic Analysis of Frames , 2000 .

[27]  Donald W. White,et al.  Displacement, Flexibility, and Mixed Beam – Column Finite Element Formulations for Distributed Plasticity Analysis , 2005 .

[28]  Byung Chai Lee,et al.  GEOMETRICALLY NON-LINEAR AND ELASTOPLASTIC THREE-DIMENSIONAL SHEAR FLEXIBLE BEAM ELEMENT OF VON-MISES-TYPE HARDENING MATERIAL , 1996 .

[29]  Enrico Spacone,et al.  Localization Issues in Force-Based Frame Elements , 2001 .

[30]  Ralph Johnson,et al.  design patterns elements of reusable object oriented software , 2019 .

[31]  Gregory L. Fenves,et al.  An object-oriented software design for parallel structural analysis , 2000 .

[32]  William McGuire,et al.  Modified Tangent Modulus Approach, A Contribution to Plastic Hinge Analysis , 2002 .

[33]  Y. Bozorgnia,et al.  Methods of Analysis for Earthquake-Resistant Structures , 2004 .

[34]  M. V. Sivaselvan,et al.  Collapse Analysis: Large Inelastic Deformations Analysis of Planar Frames , 2002 .

[35]  Filip C. Filippou,et al.  Evaluation of Nonlinear Frame Finite-Element Models , 1997 .

[36]  F. Filippou,et al.  Mixed formulation of nonlinear beam finite element , 1996 .