Invariant isogeometric formulation for the geometric stiffness matrix of spatial curved Kirchhoff rods

The steel bent frame structure of single-story factory buildings is actually a spatial structure system. Different bent frame columns are connected with the roof of bent frame structure, making the columns work and bearing the load together. In the steel frame of the factory building with bridge cranes below 20 t, variable-section columns with corbels are used to bear the crane load. In this article, the steel bent frame column of single-story factory buildings was taken as the research object. The bent frame column was simplified as a cantilever variable stepped column bearing a transverse concentrated force at the top. After simplifying the model, the theoretical formula of deflection, rotating angle, and bending moment of the compression rod was put forward. Moreover, bending deformation and stability of variable stepped columns were analyzed in order to obtain the theoretical and practical formula, then the ANSYS software was used to simulate the bent column.

Nonlinear Analysis of Steel Structure Bent Frame Column Bearing Transverse Concentrated Force at the Top in Factory Buildings

Application of 'advanced analysis' methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A research project has been conducted with the aim of developing concentrated plasticity methods suitable for practical advanced analysis of steel frame structures comprising non-compact sections. A primary objective was to produce a comprehensive range of new distributed plasticity analytical benchmark solutions for verification of the concentrated plasticity methods. A distributed plasticity model was developed using shell finite elements to explicitly account for the effects of gradual yielding and spread of plasticity, initial geometric imperfections, residual stresses and local buckling deformations. The model was verified by comparison with large-scale steel frame test results and a variety of existing analytical benchmark solutions. This paper presents a description of the distributed plasticity model and details of the verification study.

Distributed plasticity analysis of steel frame structures comprising non-compact sections

The paper presents analytical solutions for the buckling of single beams as well as two- and three-member frames subjected to torques at the supports. The governing equations and their solutions are stated, including boundary conditions and continuity conditions at connections between members, and buckling solutions are provided for a wide range of support conditions and frame geometries. The cross-section is assumed to be solid or hollow and accordingly, warping effects are ignored. The presented solutions are for a solid rectangular cross-section, and different aspect ratios are analysed to investigate the effect of changing the ratio between the minor and major second moments of area on the buckling torque and associated buckling mode. Solutions are provided for both the critical mode and higher-order modes, allowing mode-changes between symmetric and asymmetric modes to be identified. 

Analytical solutions for buckling of space frames subjected to torsional loadings

A finite element formulation for the large‐deformation analysis of space‐frame structures is presented. The formulation is based on second‐order geometric nonlinear theory and Vlasov's theory for thin‐walled beams (i.e., large displacement of members with small strains, which includes the warping deformation influence). The influence of member‐distributed loading on the geometric nonlinear response of space‐frame structures also is included. An updated Lagrangian formulation is used to model large joint translations and rotations. Prismatic beams of arbitrary cross section are considered. Rodriguez's modified rotation vector is used to represent angular deformations, which avoids rotational discontinuities at the joints of deformed space‐frame structures. Numerical results and algorithmic details are presented in a companion paper.

Closure of "Thin-Walled Space Frames. I: Large-Deformation Analysis Theory"

Based on the continuum mechanics principles, a rigorous formulation is presented for the linearized stiffness equation of three-dimensional beam elements with account taken of the joint moment equilibrium in the deformed configuration C 2  By sticking to the Bernoulli–Euler hypothesis of plane sections and elasticity definitions for stress resultants, the bending moments and torque of the element are shown to be quasi- and semi-tangential, respectively, in the updated Lagrangian formulation Further, by invoking the moment equilibrium conditions for structural nodes at C 2 , the induced moment matrix that first appears to be antisymmetric on the element level turns out to be symmetric upon assembly of all elements on the structural level The joint equilibrium conditions at C 2 , as represented by the induced moment matrix, are central not only to the out-of-plane buckling analysis of angled frames, but also to the simulation of curved beams by the straight-beam elements Examples on the buckling of angled frames and curved beams are provided to support the theory presented

Rational nonlinear analysis of framed structures and curved beams considering joint equilibrium in deformed state

Nonlinear analysis of structures is an effective way for predicting the bearing capacity or ultimate strength of a structure. This paper will review researches on the nonlinear, buckling, postbuckling and elasto-plastic analyses of three-dimensional (3D) framed structures. Also considered are curved beams since they share the problem of joint equilibrium in simulation. The following are the key issues to be covered in this paper: (a) analytical or semi-analytical approaches; (b) formulation for incremental-iterative nonlinear analysis; (c) joint equilibrium of 3D frames at the deformed configuration; (d) rigid body test for nonlinear finite elements; (e) rigid-body-qualified geometric stiffnesses and derivation; (f) simulation of buckling of curved beams; (g) elasto-plastic analysis of steel frames; (h) mechanism of iterations in incremental analysis; (i) recovery of element forces; and (j) path-tracing scheme for the postbuckling response. In this paper, the theories and methods for solving the postbuckling responses of structures involving multi-loop curves are considered. In fact, the incremental-iterative procedure for the geometric and/or inelastic nonlinear analysis can be greatly simplified if it is well rooted in physics. Namely, if the rigid body rule is fully obeyed at each stage of analysis, then the entire incremental-iterative procedure can be made simpler and more efficient. Recently, it was demonstrated that satisfactory results can be obtained for the postbuckling response of a number of structures using the elastic stiffness alone. A total of 154 references are cited in this paper.

Song He

Papers

Rational nonlinear analysis of framed structures and curved beams considering joint equilibrium in deformed state

Research on nonlinear, postbuckling and elasto-plastic analyses of framed structures and curved beams