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Direct stiffness method
About: Direct stiffness method is a research topic. Over the lifetime, 2584 publications have been published within this topic receiving 53131 citations.
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TL;DR: In this article, a framework based on the direct stiffness method for nonlinear thermo-mechanical analysis of reinforced concrete plane frames subjected to fire is presented, which accounts for geometric nonlinearity.
Abstract: This article presents a framework based on the direct stiffness method for nonlinear thermo-mechanical analysis of reinforced concrete plane frames subjected to fire. It accounts for geometric nonl...
12 citations
TL;DR: In this article, it was shown empirically that the coefficients of the polynomial in the denominator were numerically equal to the square of the determinants of the statics matrices of the respective statically determinate substructures.
12 citations
TL;DR: In this paper, the authors present a modeling technique for the nonlinear analysis of composite steel-concrete beams with partial shear interaction, which is based on the secant method, with the convergence criteria relying on the ratios of the Euclidean norms of both forces and displacements.
Abstract: This paper presents a modelling technique for the nonlinear analysis of composite steel-concrete beams with partial shear interaction. It extends the applicability of two stiffness elements previously derived by the authors using the direct stiffness method, i.e. the 6DOF and the 8DOF elements, to account for material nonlinearities. The freedoms are the vertical displacement, the rotation and the slip at both ends for the 6DOF stiffness element, as well as the axial displacement at the level of the reference axis for the 8DOF stiffness element. The solution iterative scheme is based on the secant method, with the convergence criteria relying on the ratios of the Euclidean norms of both forces and displacements. The advantage of the approach is that the displacement and force fields of the stiffness elements are extremely rich as they correspond to those required by the analytical solution of the elastic partial interaction problem, thereby producing a robust numerical technique. Experimental results available in the literature are used to validate the finite element proposed in the paper. For this purpose, those reported by Chapman and Balakrishnan (1964), Fabbrocino et al. (1998, 1999) and Ansourian (1981) are utilised; these consist of six simply supported beams with a point load applied at mid-span inducing positive bending moment in the beams, three simply supported beams with a point load applied at mid-span inducing negative bending moment in the beams, and six two-span continuous composite beams respectively. Based on these comparisons, a preferred degree of discretisation suitable for the proposed modelling technique expressed as a function of the ratio between the element length and depth is proposed, as is the number of Gauss stations needed. This allows for accurate prediction of the nonlinear response of composite beams.
12 citations
TL;DR: In this paper, a theoretical study on the dynamic stabilisation of an unstable mechanical structure is performed, where the system is unstable due to negative damping introduced by, for example, a self-excitation of linearised van der Pol type.
12 citations
TL;DR: In this article, a finite segment method is applied to solve biaxially loaded reinforced concrete columns, where the column is treated as a space structure after segmentation, and the sections are divided into finite elements of steel and concrete in order to calculate its tangent stiffnesses properties at different levels of strain.
Abstract: The finite segment method is applied here to solve biaxially loaded reinforced concrete columns. The column is treated as a space structure after segmentation. The sections are divided into finite elements of steel and concrete in order to calculate its tangent stiffnesses properties at different levels of strain. The segment stiffness relationship is computed by solving the governing differential equations about the principal axes of the cross section. Direct stiffness method is utilized to construct the whole column stiffness matrix (master stiffness matrix). Nonlinearities due to material plasticity and geometrical change are handled by an iterative procedure based on the modified tangent stiffness approach. Comparisons of failure load and deflection with biaxially loaded reinforced concrete column tests show an excellent correlation between theory and test data.
12 citations