LARGE DEFORMATIONAL ANALYSES FOR PLATE &amp; SHELL STRUCTURES BY THE TANGENT STIFFNESS METHOD

Obiya, Hiroyuki; Goto, Shigeo; Ijima, Katsushi; Iguchi, Shin-ichi

doi:10.2208/jscej.1998.598_347

Cited by 2 publications

(2 citation statements)

References 16 publications

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“…Since the rigid body rotation about an arbitrarily selected point 0 of each subdomain is gen-erally not known, the direction cosines T have to be guessed for each iterative step by an appropriate rule so as to satisfy Eqs. (6) and (7) as closely as possible. The rigid body displacements of the subdomains are not identical, and hence, a node shared by neighboring subdomains in the original state may be separated after the rigid body displacements.…”

Section: Solution Procedures (1) Basic Solution Technique By Iterationmentioning

confidence: 99%

“…The base vectors at an arbitrarily selected point 0 in each subdomain V(m) in the final equilibrium state are denoted by G The notation () indicates the value of a quantity at the point 0. Since the base vectors G are almost orthogonal unit vectors with errors of the order of small strains, a set of orthe conditions given by Eqs (6). and(7)is selected for each subdomain V(m).…”

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confidence: 99%

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Solution of Finite-Displacement Small-Strain Elasticity Problems by Removal of Rigid Body Displacements

Nishino

Malla

Sakurai

2000

Doboku Gakkai Ronbunshu

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If rigid body displacements are properly separated from a fmite-displacement small-strain problem, the remaining deformation is within the scope of the small displacement theory. For this purpose, the rigid body displacement of each sufficiently small subdomain of an elastic body must be removed independently from other subdomains before the actual deformation occurs. This paper presents a rigorous and straightforward theoretical formulation for a numerical solution procedure based on this concept. The simplicity of the formulation is due to the fact that it is developed for a general three-dimensional solid rather than structural elements as in the past works.

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Section: Solution Procedures (1) Basic Solution Technique By Iterationmentioning

confidence: 99%

mentioning

confidence: 99%

Solution of Finite-Displacement Small-Strain Elasticity Problems by Removal of Rigid Body Displacements

Nishino

Malla

Sakurai

2000

Doboku Gakkai Ronbunshu

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A Comparison for the Simulation of Frictionless Contact Problem with Large Displacement

Nizam

Obiya

Ijima

et al. 2015

AMM

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Abstract. Studies of contact problem have been widely executed by researchers with variable scopes, methods and definitions. A common problem that occurs while handling contact phenomena is sliding through element boundary [1], due to the discontinuity of the local coordinate between elements and a contact point [2] [3]. This common problem that occurs at an element boundary is such that a stable convergence result is not easily obtained. [4], thus inspires authors to make a comparison of two beam methods which are Euler-Bernoulli beam theory and Timoshenko beam theory for frictionless contact problem. The authors have been investigate geometrically non-linear analysis with extremely large displacement by the aid of Tangent Stiffness Method (TSM) [5], a robust non-linear analysis method to execute analysis and produce results with high accuracy. In this study, the authors propose the modification of beam elements with three nodes by considering the adaptation of shear deformation by Timoshenko beam theory. The modification enables the contact point to slide through the element edge smoothly and some numerical examples are provided in this study. Tangent Stiffness MethodThe TSM was solely idealized to overcome numerical cases exhibiting significant nonlinearity. The superiority of this method is that it converges the unbalanced force with high accuracy by defining element behavior using a simple form of the element force equation. This theory requires the element edge forces to be treated separately and independently of each other. In addition, strict compatibility and an equilibrium equation are disseminated in the iteration configuration to converge the unbalanced force.Here, let an element constituted by two edges with its element edge forces and the force vector for both edges is assumed as S. Let the external force vector as U, in a plane coordinate system with J as the equilibrium matrix, and the equilibrium condition could be expressed as the following equation.With the differentiation of Eq. (1), the tangent stiffness equation could be expressed as;Here, the differentiation of Eq. (1) simultaneously extract δS and δJ makes it possible to express a linear function of displacement vector, δd in the local coordinate system. Meanwhile, in Eq. (2), K O represents the element stiffness matrix which also simulates the element behavior, correspondent to the element stiffness in the coordinate system while K G , represents the element displacement originated by the tangent geometrical stiffness.

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LARGE DEFORMATIONAL ANALYSES FOR PLATE & SHELL STRUCTURES BY THE TANGENT STIFFNESS METHOD

Cited by 2 publications

References 16 publications

Solution of Finite-Displacement Small-Strain Elasticity Problems by Removal of Rigid Body Displacements

Solution of Finite-Displacement Small-Strain Elasticity Problems by Removal of Rigid Body Displacements

A Comparison for the Simulation of Frictionless Contact Problem with Large Displacement

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