Recent scientific and computational advances have facilitated the analysis of slender structural systems subject to instability. With the employment of more sophisticated numerical tools and algorithms, it is possible to accurately determine the critical points (limit and bifurcation loads) as well as the post-critical behavior of the structural system. In the computational context, efficient data structures are needed to enable code and graphic interface expansion for the generation of models and visualization of the results obtained. Thus, an interactive object-orientated graphic computational system is presented herein. It has been developed using MATLAB/GUI, with pre-processing, analysis and post-processing capacities for planar structural frames. The nonlinear finite element developed and implemented for the structure modeling is formulated considering second order effects. Therefore, with the computational tool presented, the geometric nonlinear effects and stability of the structural system can be directly addressed, and the visualization of the numerical results are accessed through interactive controls that permit data inclusion and analysis verification. The engineerdesigner can see the structural model discretization, the equilibrium path, its deformation configuration, the force and bending moment diagrams at the moment that he runs the program and in each load step. It is also possible to export the images, videos or tables of the obtained numerical results. The example presented demonstrates the capacity of the developed graphic computational system.

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This article describes a novel equilibrium-based geometrically exact beam finite element formulation. First, the spatial position and rotation fields are interpolated by nonlinear configuration-dependent functions that enforce constant strains along the element axis, completely eliminating locking phenomena. Then, the resulting kinematic fields are used to interpolate the spatial sections force and moment fields in order to fulfill equilibrium exactly in the deformed configuration. The internal variables are explicitly solved at the element level and closed-form expressions for the internal force vector and tangent stiffness matrix are obtained, allowing for explicit computation, without numerical integration. The objectivity and absence of locking are verified and some important numerical and theoretical aspects leading to a computationally efficient strategy are highlighted and discussed. The proposed formulation is successfully tested in several numerical application examples.

Abstract. The analysis of pyramidal trusses has an immediate practical interest since these structures are currently used in many present-day civil constructions, either as main parts or a constitutive element. They can be used to represent tripod-like structures, cap of masts, tower cranes, big span roofs, and even a portion of a single-layer geodesic dome or of a generic-shaped reticulated shell. This paper examines the nonlinear static stability and load capacity for a simple class of space trusses in the shape of a regular pyramid. Joints located at the vertices of the base polygon are fixed while the joint at the apex is subjected to static loads acting in either the vertical direction, in the horizontal plane, or along a generic oblique direction. Despite their apparent simplicity, these structural systems exhibit a wide variety of post-critical responses, not exhausted by the classical snapping and bifurcation phenomena. In addition to regular primary and secondary branches, the equilibrium paths may include neutral branches, namely branches entirely composed of bifurcation or limit points. The analysis is conducted using the Finite Element Method together with a corotational formulation for the bars. The numerical results are validated in the elastic domain using the closed-form solutions found in literature.