A two-field mix variational principle for partially connected composite beams

This paper presents a new beam-column element for the nonlinear analysis of partially connected composite beams. The element is based on a two-field mixed variational principle, where both variables, forces and deformations, are simultaneously approximated within the element. The model neglects uplift and frictional effects. Shear connectors are modeled using a distributed interface element. Two algorithms for the proposed model are presented. Stability of both algorithms is discussed. Numerical examples that clarify the advantages of the proposed model over standard models based on the principle of minimum potential energy, and discuss the different alternatives of the order of interpolation functions are presented. The studies prove the superiority of the mixed model.

[1]  Tateo Kajita,et al.  Elastic-plastic analysis of composite beams with incomplete interaction by finite element method , 1981 .

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

[3]  B. D. Veubeke.  Displacement and equilibrium models in the finite element method , 1965 .

[4]  F. Brezzi.  On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers , 1974 .

[5]  A. G. Razaqpur,et al.  A finite element for modelling the nonlinear behavior of shear connectors in composite structures , 1989 .

[6]  M.J.S. Hirst,et al.  The analysis of composite beams using standard finite element programs , 1980 .

[7]  J. Z. Zhu,et al.  The finite element method , 1977 .

[8]  Faker Ben Belgacem,et al.  The Mortar finite element method with Lagrange multipliers , 1999, Numerische Mathematik.

[9]  I. Babuska.  The finite element method with Lagrangian multipliers , 1973 .

[10]  Ivan M. Viest,et al.  Composite Construction Design for Buildings , 1996 .

[11]  Giorgio Monti,et al.  FINITE ELEMENT FOR ANCHORED BARS UNDER CYCLIC LOAD REVERSALS , 1997 .

[12]  S. Timoshenko,et al.  Analysis of Bi-Metal Thermostats , 1925 .

[13]  A. W. Wegmuller,et al.  Nonlinear response of composite steel-concrete bridges , 1977 .

[14]  Filip C. Filippou,et al.  A Model for Composite Steel-Concrete Girders under Cyclic Loading , 1997 .

[15]  Ping Kock Ma.  Inelastic Analysis of Composite Beams with Partial Connection , 1973 .

[16]  Krishna S. Naraine,et al.  Slip and Uplift Effects in Composite Beams , 1984 .

[17]  F. Filippou,et al.  MIXED FORMULATION OF BOND-SLIP PROBLEMS UNDER CYCLIC LOADS , 1999 .

[18]  R. Park,et al.  Stress-Strain Behavior of Concrete Confined by Overlapping Hoops at Low and High Strain Rates , 1982 .

[19]  Michel Crisinel,et al.  Composite Slab Behavior and Strength Analysis. Part I: Calculation Procedure , 1993 .

[20]  Enrico Spacone,et al.  FIBRE BEAM–COLUMN MODEL FOR NON‐LINEAR ANALYSIS OF R/C FRAMES: PART I. FORMULATION , 1996 .

[21]  Dan M. Frangopol,et al.  Nonlinear Analysis of Composite Beams with Deformable Shear Connectors , 1998 .

[22]  A. O. Adekola,et al.  Partial interaction between elastically connected elements of a composite beam , 1968 .

[23]  Ashraf Ayoub,et al.  MIXED FORMULATION OF NONLINEAR STEEL-CONCRETE COMPOSITE BEAM ELEMENT , 2000 .