• Structural Engineering and Mechanics
• /
• v.13 no.4
• /
• pp.437-453
• /
• 2002

In this paper, dynamic stiffness and flexibility for circular membranes are analytically derived using an efficient mixed-part dual boundary element method (BEM). We employ three approaches, the complex-valued BEM, the real-part and imaginary-part BEM, to determine the dynamic stiffness and flexibility. In the analytical formulation, the continuous system for a circular membrane is transformed into a discrete system with a circulant matrix. Based on the properties of the circulant, the analytical solutions for the dynamic stiffness and flexibility are derived. In deriving the stiffness and flexibility, the spurious resonance is cancelled out. Numerical aspects are discussed and emphasized. The problem of numerical instability due to division by zero is avoided by choosing additional constraints from the information of real and imaginary parts in the dual formulation. For the overdetermined system, the least squares method is considered to determine the dynamic stiffness and flexibility. A general purpose program has been developed to test several examples including circular and square cases.

• Journal of the Korea institute for structural maintenance and inspection
• /
• v.15 no.2
• /
• pp.125-135
• /
• 2011

The latest study for formulation of finite element method and computation techniques has progressed widely. The classical method in the formulation of frame elements for geometrically nonlinear analysis derives the geometric stiffness directly from the governing differential equation for bending with axial force. From the computational viewpoint of this paper, the most common approach is the finite element method. Commonly, the formulation of frame elements for geometrically nonlinear structures is based on appropriate interpolation functions for the transverse and axial displacements of the member. The formulation of flexibility-based elements, on the other hand, is based on interpolation functions for the internal forces. In this paper, a new method is used to suppose that interpolation functions for the displacements from the curvatures is Lagrangian interpolation. This paper derives flexibility matrix from that displacement functions and is considered the application of it. Using the flexibility matrix, this paper apply the program considered geometrically nonlinear analysis to common problems.

• Structural Engineering and Mechanics
• /
• v.8 no.3
• /
• pp.257-272
• /
• 1999

In this paper a simple finite element is proposed for analyzing out of plane vibration of thin walled curved beams, with both open and closed sections, considering shear flexibility. The present element is obtained from a variational formulation governing the dynamics of a three-dimensional elastic body in which the stress tensor as well as the displacements are variationally independent. The element has two nodes with four degrees of freedom in each. Numerical examples for the first six frequencies are performed in order to assess the accuracy of the finite element formulation and to show the influence of the shear flexibility on the dynamics of the member.

• Computers and Concrete
• /
• v.6 no.5
• /
• pp.377-390
• /
• 2009

In this paper an improved one-dimensional frame element for modelling of reinforced concrete beams and columns subjected to impact is presented. The model is developed in the framework of a flexibility fibre element formulation that ignores the shear effect at material level. However, a simple shear cap is introduced at section level to take account of possible shear failure. The effect of strain rate at the fibre level is taken into account by using the dynamic increase factor (DIF) concept for steel and concrete. The capability of the formulation for estimating the element response history is demonstrated by some numerical examples and it is shown that the developed 1D element has the potential to be used for dynamic analysis of large framed structures subjected to impact of air blast and rigid objects.

• Structural Engineering and Mechanics
• /
• v.56 no.2
• /
• pp.169-188
• /
• 2015

There are two types of nonlinear analysis methods for building frameworks depending on the method of modeling the plastification of members including lumped plasticity and distributed plasticity. The lumped plasticity method assumes that plasticity is concentrated at a zero-length plastic hinge section at the ends of the elements. The distributed plasticity method discretizes the structural members into many line segments, and further subdivides the cross-section of each segment into a number of finite elements. When a reinforced concrete member experiences inelastic deformations, cracks tend to spread form the joint interface resulting in a curvature distribution. The program IDARC includes a spread plasticity formulation to capture the variation of the section flexibility, and combine them to determine the element stiffness matrix. In this formulation, the flexibility distribution in the structural elements is assumed to be the linear. The main objective of this study is to evaluate the accuracy of linear flexibility distribution assumed in the spread inelasticity model. For this purpose, nonlinear analysis of two reinforced concrete frames is carried out and the linear flexibility models used in the elements are compared with the real ones. It is shown that the linear flexibility distribution is incorrect assumption in cases of significant gravity load effects and can be lead to incorrect nonlinear responses in some situations.

• Structural Engineering and Mechanics
• /
• v.5 no.5
• /
• pp.523-528
• /
• 1997

Stiffness and flexibility equations are combined in the buckling analysis of a braced structure - stiffness for the original structure and flexibility for the bracing. Choosing a flexibility formulation for the bracing gives a very compact computational problem. It also gives theoretical insights into the behaviour of the braced structure.

• Structural Engineering and Mechanics
• /
• v.36 no.1
• /
• pp.57-78
• /
• 2010

A novel flexibility-based 1D element that captures the material nonlinearity and second order P-$\Delta$ effects within a reinforced concrete frame member is developed. The formulation is developed for 2D planar frames in the modified fiber element framework but can readily be extended to 3D cases. The nonlinear behavior of concrete including cracking and crushing is taken into account through a modified hypo-elastic model. A parabolic and a constant shear stress distribution are used at section level to couple the normal and tangential tractions at material level. The lack of objectivity due to softening of concrete is addressed and objectivity of the response at the material level is attained by using a technique derived from the crack band approach. Finally the efficiency and accuracy of the formulation is compared with experimental results and is demonstrated by some numerical examples.

• Structural Engineering and Mechanics
• /
• v.42 no.1
• /
• pp.39-53
• /
• 2012

This paper presents an alternative way to derive the exact element stiffness matrix for a beam on Winkler foundation and the fixed-end force vector due to a linearly distributed load. The element flexibility matrix is derived first and forms the core of the exact element stiffness matrix. The governing differential compatibility of the problem is derived using the virtual force principle and solved to obtain the exact moment interpolation functions. The matrix virtual force equation is employed to obtain the exact element flexibility matrix using the exact moment interpolation functions. The so-called "natural" element stiffness matrix is obtained by inverting the exact element flexibility matrix. Two numerical examples are used to verify the accuracy and the efficiency of the natural beam element on Winkler foundation.

• Geomechanics and Engineering
• /
• v.24 no.4
• /
• pp.371-388
• /
• 2021

A novel flexibility-based beam-foundation model for inelastic analyses of beams resting on foundation is presented in this paper. To model the deformability of supporting foundation media, the Winkler-Pasternak foundation model is adopted. Following the derivation of basic equations of the problem (strong form), the flexibility-based finite beam-foundation element (weak form) is formulated within the framework of the matrix virtual force principle. Through equilibrated force shape functions, the internal force fields are related to the element force degrees of freedom. Tonti's diagrams are adopted to present both strong and weak forms of the problem. Three numerical simulations are employed to assess validity and to show effectiveness of the proposed flexibility-based beam-foundation model. The first two simulations focus on elastic beam-foundation systems while the last simulation emphasizes on an inelastic beam-foundation system. The influences of the adopted foundation model to represent the underlying foundation medium are also discussed.

• Journal of Korea Society of Industrial Information Systems
• /
• v.26 no.3
• /
• pp.9-22
• /
• 2021

This study proposes a supply chain network (SCN) model considering supply disruption in assembly industry. For supply disruption, supplier disruption and its route disruption are simultaneously taken into consideration in the SCN model. With the simultaneous consideration, the SCN model can achieve its flexibility and efficiency. A mathematical formulation is suggested for representing the SCN model, and a proposed hybrid genetic algorithm (pro-HGA) is used for implementing the mathematical formulation. In numerical experiment, the performance of the pro-HGA approach is compared with those of some conventional approaches using the SCN models with various scales, and a sensitivity analysis considering the change of the numbers of suppliers and backup routes is done. Experimental results show that the performances of the pro-HGA approach are superior to those of the conventional approaches, and the flexibility and efficiency of the SCN model considering supply disruption are proved. Finally, the significance of this study is summarized and a potential future research direction is mentioned in conclusion.