• Journal of Mechanical Science and Technology
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• v.18 no.9
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• pp.1529-1536
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• 2004

A structure is broken down into a number of substructures by means of the finite element method and the substructures are synthesized for the complete structure. The divided substructures take two types: fixed-free and free-free elements. The flexibility and stiffness matrices of the free-free elements are the Moore-Penrose inverse of each other. Thus, it is not easy to determine the equilibrium equations of the complete structure composed of two mixed types of substructures. This study provides the general form of equilibrium equation of the entire structure through the process of assembling the equilibrium equations of substructures with end conditions of mixed types. Applications demonstrate that the proposed method is effective in the structural analysis of geometrically complicated structures.

• Proceedings of the Korea Concrete Institute Conference
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• 1990.10a
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• pp.7-12
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• 1990

This paper presents an equation for balanced-steel ratio in longitudinal and transverse direction throughout analysis based on a space truss model introducing the concept of concrete softening effect. This paper also presents as equation for postcracking torisonal stiffness throughout analysis considering the equilibrium conditions and compatibility conditions based on shear panel. Correlation between predicted postcracking torsional stiffness, and experimental results was good, not only for beams tested in this paper but also for others in the literature.

• Proceedings of the Korea Concrete Institute Conference
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• 1991.10a
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• pp.51-58
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• 1991

In staically indeterminate structures torsional stiffness is an important factor for prediction of mechanical behavior at all loading stages in reinfored concrete beams, which also for calculation of torsional moment. This paper proposes equation for postcracking torsional stiffness of reinforced concrete beams under pure torsion, which is derived considering the equilibrium and compatibility condition for shear panel based on the variable angle space truss model. The equation describes well the effect according to the variation of aspect ratio and steel volume ratio per unit concrete volume. It agress with experimental results in this paper as well as available literature.

• Structural Engineering and Mechanics
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• v.3 no.4
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• pp.299-312
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• 1995

A new reinforcing steel model which is embedded inside a concrete element and also accounts for the effect of bond-slip is developed. Unlike the classical bond-link or bond-zone element using double nodes, the proposed model is considering the bond-slip effect without taking double nodes by incorporation of the equivalent steel stiffness. After calculation of nodal displacements, the deformation of steel at each node can be found through the back-substitution technique from the first to the final steel element using a governing equation constructed based on the equilibrium at each node of steel and the compatibility condition between steel and concrete. This model results in significant savings in the number of nodes needed to account for the effect of bond-slip, in particular, when the model is used for three dimensional finite element problems. Moreover a new nonlinear solution scheme is developed in connection with this model. Finally, correlation studies between analytical and experimental results and several parameter studies are conducted with the objective to establish the validity of the proposed model.

• Interaction and multiscale mechanics
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• v.1 no.3
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• pp.329-337
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• 2008

This paper presents the derivation of the generalized governing equations in theory of elasticity, their weak forms and the some applications in the numerical analysis of structural mechanics. Unlike the differential equations in classical elasticity theory, the generalized equations of the equilibrium and compatibility equations presented here take the form of integral equations, and the generalized equilibrium equations contain the classical differential equations and the boundary conditions in a single equation. By using appropriate test functions, the weak forms of these generalized governing equations can be established. It can be shown that various variational principles in structural analysis are merely the special cases of these weak forms of generalized governing equations in elasticity. The present weak forms of elasticity equations extend greatly the choices of the trial functions for approximate solutions in the numerical analysis of various engineering problems. Therefore, the weak forms of generalized governing equations in elasticity provide a powerful modeling tool in the computational structural mechanics.

• Journal of the Korea Concrete Institute
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• v.14 no.6
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• pp.1010-1021
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• 2002

The current ACI design code does not take into account the contribution of concrete for the torsional moment of reinforced concrete(RC) beams subjected to pure torsion. This code is not capable of evaluating the inter-effects between concrete and torsional reinforcement on the torsional resistance of the RC beams. Some test results indicated that the current ACI code was not successful in predicting the observed torsional moment of the RC beams with reasonable accuracy. The research reported in this paper provides an evaluation equation to predict the torsional moment of the RC beams subjected to pure torsion. The proposed equation is derived from the equilibrium as well as compatibility equations of the truss model for the cracked RC beams. Comparisons between the observed and calculated torsional moments of the 66 tested beams, showed reasonable agreement.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.1A
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• pp.55-65
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• 2006

This paper presents the closing analysis of a symmetric steel cable-stayed bridge erected by a free cantilever method. Two independent structural systems are formed before the closing procedure of a bridge is performed, and thus the compatibility conditions for vertical displacement and rotational angle are not satisfied at the closing section without the application of proper sectional forces. Since, however, it is usually impossible to apply sectional forces at the closing section, the compatibility conditions should be satisfied by proper external forces that can be actually applicable to a bridge. Unstrained lengths of selected cables and the pull-up force of a derrick crane are adjusted to satisfy nonlinear compatibility conditions, which are solved iteratively by the Newton-Raphson method. Cable members are modeled by the elastic catenary cable elements, and towers and main girders are discretized by linear 3-D frame elements. The sensitivities of displacement with respect to the unstrained lengths of selected cables and the pull-up force of the derrick crane are evaluated by the direct differentiation of the equilibrium equation. A Monte-Carlo simulation approach is proposed to estimate expected construction errors for a given confidence level. The proposed method is applied to the second Jindo Grand Bridge to demonstrate its validity and effectiveness.

• Ocean and Polar Research
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• v.42 no.1
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• pp.77-88
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• 2020

This paper presents the coordinate systems used for trawl doors modeling, and provides matrix equations of connection between these systems. The projections of the forces acting on the door into axes of various coordinate systems were obtained, which were used in the door equilibrium equations. Six equilibrium conditions for the door as a solid were obtained: formulas that allow for the door area in plan to be determined; its weight in water; its mass; three moment equations for determining the position of the warp and backstrops fastening points to the door with triangular and quadrangular backstrop arrangements. It was found that the moment equilibrium equations of trawl doors are generally incompatible, which was not found by any of the authors who have previously conducted research into trawl doors. Using the Kronecker-Capelli theorem, the compatibility equation is obtained. This equation includes the coordinates of the backstrop fastening points to the door, which means that these points cannot be randomly selected. The technique of determining the warp and backstrops' fastening points position to the door is described. Conditions of directional (by angle of attack) and roll (in angle of roll) stability of the doors' equilibrium are presented. The equations presented in this paper comprise a mathematical model that allows, when designing the doors, to select optimal parameters, as well as to carry out adjustments for trawling purposes to ensure the stable movement of the doors and the entire trawl system.

• Structural Engineering and Mechanics
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• v.31 no.2
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• pp.181-210
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• 2009

This paper presents the theoretical developments of an exact finite strip for the buckling and initial post-buckling analyses of isotropic flat plates. The so-called exact finite strip is assumed to be simply supported out-of-plane at the loaded ends. The strip is developed based on the concept that it is effectively a plate. The present method, which is designated by the name Full-analytical Finite Strip Method in this paper, provides an efficient and extremely accurate buckling solution. In the development process, the Von-Karman's equilibrium equation is solved exactly to obtain the buckling loads and the corresponding form of out-of-plane buckling deflection modes. The investigation of thin flat plate buckling behavior is then extended to an initial post-buckling study with the assumption that the deflected form immediately after the buckling is the same as that obtained for the buckling. It is noted that in the present method, only one of the calculated out-of-plane buckling deflection modes, corresponding to the lowest buckling load, i.e., the first mode is used for the initial post-buckling study. Thus, the postbuckling study is effectively a single-term analysis, which is attempted by utilizing the so-called semi-energy method. In this method, the Von-Karman's compatibility equation governing the behavior of isotropic flat plates is used together with a consideration of the total strain energy of the plate. Through the solution of the compatibility equation, the in-plane displacement functions which are themselves related to the Airy stress function are developed in terms of the unknown coefficient in the assumed out-of-plane deflection function. These in-plane and out-of-plane deflected functions are then substituted in the total strain energy expressions and the theorem of minimum total potential energy is applied to solve for the unknown coefficient. The developed method is subsequently applied to analyze the initial postbuckling behavior of some representative thin flat plates for which the results are also obtained through the application of a semi-analytical finite strip method. Through the comparison of the results and the appropriate discussion, the knowledge of the level of capability of the developed method is significantly promoted.

• Wind and Structures
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• v.3 no.4
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• pp.291-302
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• 2000

A new finite element technique to solve the problem of wind and structure interactions is presented. Conventionally, wind analysis is performed on the Eulerian description in which the finite element mesh would not move in accordance with the wind flow. However, it is not the case in wind-structure interaction problems because nodes attached to the surface of structure should move with the displacement of structure. The arbitrary Lagrangian-Eulerian (ALE) method treats the mesh and flow independently, and allow the mesh to move. In this study, the analysis domain is divided into regions of the structure, air around the structure and the interface of two regions. To satisfy the compatibility and equilibrium conditions between separated regions and to carry out the efficient analysis, the rigid link is used. Also the equation of wind and that of structure are arranged in a single matrix equation.