Topic
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.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, a uniform linearly elastic beam element with non-coinciding centers of geometry, shear and mass is studied under stationary harmonic end excitation, and the Euler-Bernoulli-Saint Venant theory is applied.
Abstract: A uniform linearly elastic beam element with non-coinciding centres of geometry, shear and mass is studied under stationary harmonic end excitation. The Euler-Bernoulli-Saint Venant theory is applied. Thus the effect of warping is not taken into account. The frequency-dependent 12 × 12 element stiffness matrix is established by use of an exact method. The translational and rotational displacement functions are represented as sums (real) of complex exponential terms where the complex exponents are numerically found. Built-up structures containing beam elements of the described type can be analysed with ease and certainty using existing library subroutines.
92 citations
TL;DR: In this article, the finite element method with a cubic interpolation of the inertia forces is developed for the solution of problems in structural dynamics with a non-linear stiffness, and algorithms are given for the direct iterative solution of the equations of motion and for their solution by piecewise linearization.
92 citations
TL;DR: In this article, the authors compared approximate analytical solutions and finite element results to conclude on a simple procedure that allows for the estimation of the kinematic response functions and dynamic stiffnesses of approach embankments.
Abstract: Recognizing that soil-structure interaction affects appreciably the earthquake response of highway overcrossings, this paper compares approximate analytical solutions and finite element results to conclude on a simple procedure that allows for the estimation of the kinematic response functions and dynamic stiffnesses of approach embankments. It is shown that the shear-wedge model yields realistic estimates for the amplification functions of typical embankments and reveals the appropriate levels of dynamic strains which are subsequently used to estimate the stiffness and damping coefficients of embankments. The shear-wedge model is extended to a two-dimensional model in order to calculate the transverse static stiffness of an approach embankment loaded at one end. The formulation leads to a sound closed-form expression for the critical length, , that is the ratio of the transverse static stiffness of an approach embankment and the transverse static stiffness of a unit-width wedge. It is shown through two case studies that the transverse dynamic stiffness (“spring” and “dashpot”) of the approach embankment can be estimated with confidence by multiplying the dynamic stiffness of the unit-width wedge with the critical length, . The paper concludes that the values obtained for the transverse kinematic response function and dynamic stiffness can also be used with confidence to represent the longitudinal kinematic response function and dynamic stiffness respectively.
91 citations
TL;DR: In this paper, the structural stiffness matrix and the total potential energy of the structure are utilized to direct the rapid convergence of the structural configuration to the self-equilibrated and stable state.
91 citations
TL;DR: In this paper, exact solutions for the buckling loads of variable cross-section columns, loaded by variable axial force, for several boundary conditions are given. But they do not consider the effects of the axial load on the stiffness matrix.
91 citations