Hiroaki Katori

Consideration of the problem of shearing and torsion of thin-walled beams with arbitrary cross-section

In structural analysis it is often necessary to determine the geometrical properties of cross-sectional areas. The location of the shear center is of greater importance for a thin-walled cross-section. The purpose of this paper is the computation of the shear center of arbitrary thin-walled cross-sections using the finite element method. The coupling problem of shearing and torsional deformation of thin-walled beams based on Saint Venants theory is considered. This problem of coupled shearing and torsional deformation was analyzed using the finite element method in which the matrix of shear rigidity and torsional rigidity were determined. The shear center can be obtained by determining the coordinate axes so as to eliminate the nondiagonal terms. Then, applying the stiffness matrix of shear rigidity and torsional rigidity obtained in the above, the stiffness matrix of the space framework elements in which the shear deformation is taken into consideration is developed.

Non-conforming triangular finite element based on Mindlin plate theory

Abstract A bending theory, including the effects of transverse shear deformation, was developed by Reissner and Mindlin. Reissners and Mindlins theories are utilized to formulate finite elements in consideration of transverse shear deformation. In this paper, a triangular finite element for thin and thick plate bending is developed, based on Mindlin plate theory. We suggest a method to obtain an element stiffness matrix under the condition where the transverse shear deformation is constant within an element, and based on non-conforming elements. Several numerical experiments are performed and show that the present element gives excellent results for both thin and thick plates.

Treatment of discontinuous boundary conditions for boundary element method

Abstract In the case of analyzing various problems by means of the boundary element method, special treatment is required for corner points and discontinuous boundary conditions. In this paper, a method for reasonable treatment of discontinuous boundary conditions is proposed in the analysis of potential problems, plane stress problems and plate bending problems. Numerical examples of the present method are shown and compared with values obtained by means of other methods.

Numerical analysis of elastic-plastic bending of curved beams with thin-walled cross-section

Abstract It is well known that, when a curved beam is subject to bending, the shape of its cross-section is flattened and collapse occurs as the rigidity is reduced. It is important for design to determine the nonlinear behavior of such beams. This paper describes the elastic-plastic large deformation analysis of a curved beam with a thin-walled cross-section by the finite element method. The analytical formulation is developed by extending the kinematic work hardening model proposed by Ziegler. Several representative cases are computed.

A boundary element analysis of coupled shearing and torsional deformation of beams

Abstract In the engineering beam theory, shear deformation was neglected. A unified beam theory compensating the inconsistency caused by this, has not yet been proposed. In the present paper, the coupling problem of shearing and torsional deformation of a beam with an arbitrary cross section based on Saint Venants theory is considered, and shows that this problem becomes the boundary-value problems governed by Poissons equation. This problem of coupled shearing and torsional deformation was analyzed using the boundary element method in which the matrix of shear rigidity and torsional rigidity were determined. Taking the nondiagonal terms of the matrix equal to zero, we obtained the shear center.

A Note on the Simulation of Linkage Mechanism

The dynamic analysis of link structure, including flexible elements is developed in this study. This analysis is based on the finite element method and the direct numerical integration, and can be used to predict the dynamic response of link structures. The purpose of this report is to establish the scheme using FEM for 2-D motional link structures. Some simulation tests are carried out using the scheme and the validity is verified.

Shear Center for Thin-Walled Cross Sections.

In structural analysis it is often necessary to determine the geometrical properties of cross sectional areas. The location of the shear center is of greater importance for a thin-walled cross section.The purpose of this paper is the computation of the shear center of the arbitrary thin-walled cross sections using the finite element method. The coupling problem of shearing and torsional deformation of a thin-walled beams based on Saint Venants theory is considered. This problem of coupled shearing and torsional deformation was analyzed using the finite element method in which the matrix of shear rigidity and torsional rigidity were determined. The shear center can be obtained determining the coordinate axes so as to eliminate the nondiagonal terms.

Shear Deflection of Anisotropic Plate

In the thin plate theory, shear deformation is neglected. This theory is unreliable for plates of considerable thickness in the vicinity of the point of application of load, and sandwich plates with shear rigidity which is very low compared with bending rigidity. A widely accepted theory which includes the effects of shear deformation was developed by Reissner and Mindlin. In recent years, composite materials have been widely employed as structure elements, and it is important to understand their characteristics for designing structures. Plates of composite material are characterized by strong anisotropy and low out-of-plane shear rigidity. This paper provides a convenient representation for the stiffness matrix of the finite element in order to analyze a sandwich plate with an anisotropic face plate and core. The formulation is based on the non-conforming element of Zienkiewicz and is obtained with a modified stiffness matrix in the condition in which the out-of-plane shear strain is constant in two directions within an element.

Shear deformation in beam theory.

The elementary beam theory is based on the Bernoulli-Euler hypothesis, in which no shear deformation is allowed to occur excluding the case of torsional deformation. This theory involves some theory to be improved. We consider here a refined beam theory taking into account the effect of shear deformation. This theory may be applied to any cross section of beam using the finite element method. Next, we asked for the stiffness matrix of an element of space framework taking into account the effect of the shear deformation. Some numerical examples of the present theory are shown and compared with values obtained by other methods.

Elastic-plastic large deformation analysis of curved beam with thin walled cross section.

It is well known that when a curved beam is subject to bending, the shape of its cross section is flattened and collapse occurs as the rigidity is reduced. It is important for design determine their nonlinear behavior. This paper describes the elastic-plastic large deformation analysis of a curved beam with a thin walled cross section by the finite element method. The analytical formulation is developed by extending the kinematic work hardening model preposed by Ziegler. Several representative cases are computed.