Tangent stiffness matrix

About: Tangent stiffness matrix is a research topic. Over the lifetime, 1031 publications have been published within this topic receiving 21140 citations.

PIA for Uniform Cubic B-spline Curve Interpolation with Prescribed Tangent Vector

Abstract: An uniform cubic B-spline curve is generated to interpolate the data points with prescribed tangent vectors based on the progressive iterative approximation. It starts with an initial Bspline curve which takes the given data points as the control points with even indexes and takes the end points of the tangent vectors as the control points with odd indexes. Then by adjusting its control points gradually with iterative formulas,a sequence of curves is obtained. The limit curve of the sequence will interpolate the data points with prescribed tangent vectors. The curve fits a given ordered point set and corresponding tangent vectors without solving a linear system.

Comprehensive Stiffness of Prestressed Lattice Materials

Abstract: Several approaches to obtain the comprehensive stiffness of finite frameworks are present in literature; yet, the formulation has not been addressed for lattice materials and infinitely periodic structures. The objective of this paper is to introduce a systematic method to calculate the comprehensive stiffness of prestressed, infinitely periodic, structures and lattice materials with pin- and rigid-jointed connectivity. We first derive the comprehensive stiffness of a finite framework through the superposition of its material and nonlinear geometrical stiffness. By using the Bloch's theorem, we derive the irreducible form of the stiffness system of the finite framework, which represents the stiffness behaviour of the corresponding infinite, periodic assembly. Finally, the comprehensive stiffness of the infinite lattice is homogenized to generate the stiffness characteristics of the lattice material. A detailed example is provided to show the application of the methodology. Closed-form expressions of the elastic properties are presented for 12 planar lattices.

Semi-rigid elasto-plastic post buckling analysis of a space frame with finite rotation

Abstract: In this study, large-deformation and small-strain elasto-plastic analysis of space frames with symmetric cross sections and semi-rigid connections are presented. The effect of axial forces on the bending moment and lateral buckling are included. However, axial-torsional and warping effects are omitted. The Eulerian equations for a beam-column with finite rotation taking into account bowing effects are adopted for an elastic system and are extended to an inelastic system with a plastic hinge concept. The derived tangent stiffness matrix is asymmetric due to the finite rotation. The joint connection elements were introduced for semi-rigidity using a static condensation technique. The arc-length method was applied to trace the post-buckling range of elastic and elasto-plastic problems with semi-rigid connections. Nonlinear buckling and elasto-plastic collapse analyses were carried out for the proposed space frame to demonstrate the potential of the developed method in terms of accuracy and efficiency.