• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.04a
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• pp.103-110
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• 1996

In this paper, behaviour of underground structural systems due to excavation and change of groundwater level is analyzed using finite elements. Equilibrium equations based on the effective pressure theory and transient flow equations considering the groundwater level are derived. Integration equations are derived using Galerkin's approximation and time dependent analysis is employed to compute groundwater level change and pore pressures. This computed pore pressures are employed in equilibrium equations and then finally displacements and stresses are computed. The developed program is applied to analyze the behaviour of ground excavation below the groundwater level. The program is also applied to multi-step excavation at the same model. The results show that the displacements of the ground surface are much influenced by the change of the groundwater level. Therefore, it is concluded that the change of the groundwater level should be considered in order to analyze the behaviour of the underground structural systems accurately

• Wind and Structures
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• v.23 no.5
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• pp.421-447
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• 2016

Wind-induced and earthquake-induced excitations on tall structures can be effectively controlled by Tuned Liquid Damper (TLD). This work presents a numerical simulation procedure to study the performance of tuned liquid tank- structure system through ${\sigma}$-transformation based fluid-structure coupled solver. For this, a 'C' based computational code is developed. Structural equations are coupled with fluid equations in order to achieve the transfer of sloshing forces to structure for damping. Structural equations are solved by fourth order Runge-Kutta method while fluid equations are solved using finite difference based sigma transformed algorithm. Code is validated with previously published results. The minimum displacement of structure is observed when the resonance condition of the coupled system is satisfied through proper tuning of TLD. Since real-time excitations are random in nature, the performance study of TLD under random excitation is also carried out in which the Bretschneider spectrum is used to generate the random input wave.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.501-506
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• 2007

A generalized finite difference method for solving solid mechanics problems such as elasticity and crack problems is presented. The method is constructed in framework of Taylor polynomial based on the Moving Least Squares method and collocation scheme based on the diffuse derivative approximation. The governing equations are discretized into the difference equations and the nodal solutions are obtained by solving the system of equations. Numerical examples successfully demonstrate the robustness and efficiency of the proposed method.

• Structural Engineering and Mechanics
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• v.7 no.2
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• pp.159-180
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• 1999

The present paper shows a new non-tensorial approach to derive basic equations for various structural analyses. It can be used directly in numerical computation procedures. The aim of the paper is, however, to show that the approach serves as an excellent tool for analytical purposes also, working as a link between analytical and numerical techniques. The paper gives a method to derive, at first, expressions for strains in general beam and shell analyses, and secondly, the governing equilibrium equations. The approach is based on the utilization of local fixed Cartesian coordinate systems. Applying these, all the definitions required are the simple basic ones, well-known from the analyses in common global coordinates. In addition, the familiar principle of virtual work has been adopted. The method will be, apparently, most powerful in teaching the theories of curved beam and shell structures for students not familiar with tensor analysis. The final results obtained have no novelty value in themselves, but the procedure developed opens through its systematic and graphic progress a new standpoint to theoretical considerations.

• Journal of the Society of Naval Architects of Korea
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• v.36 no.1
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• pp.15-21
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• 1999

In this paper, the issue of local structural identifiability of linear equations of motion with non-linear parametrizations is discussed. The test method is resented that provides analytical expressions for information matrices of which the rack determines identifiability. And this method is applied to investigate local structural identifiability of linear equations of motion for a submergible vehicle. As a result, it is showed that with given parameters, the linear equations of motion do not satisfy the definition of local identifiabiliy according Glover & Willems.

• Structural Engineering and Mechanics
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• v.18 no.5
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• pp.565-589
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• 2004

The present paper concerns the macroscopic overall description of rheologic properties for steel wire and synthetic fibre cables under variable loading actions according to non-linear creep and/or relaxation theory. The general constitutive equations of non-linear creep and/or relaxation of tension elements - cables under one-step and the variable stress or strain inputs using the product and two types of additive approximations of the kernel functions are presented in the paper. The derived non-linear constitutive equations describe a non-linear rheologic behaviour of the cables for a variable stress or strain history using the kernel functions determined only by one-step - constant creep or relaxation tests. The developed constitutive equations enable to simulate and to predict in a general way non-linear rheologic behaviour of the cables under an arbitrary loading or straining history. The derived constitutive equations can be used for the various tension structural elements with the non-linear rheologic properties under uniaxial variable stressing or straining.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.619-624
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• 2007

Spectral element method (SEM) is introduced for the fully coupled structural dynamic problems, In this paper, the beam with passive constrained layered damping (PCLD) treatments is considered as a representative problems. The beam consists of a viscoelastic layer that is sandwiched between the base beam structure and an elastic layer, The fully coupled equations of motion for a PCLD beam are derived, The equations of motion are derived first by using Hamilton's principle, From this equations of motion, the spectral element is formulated for the vibration analysis by use of the SEM, As an illustrative example, a cantilevered beam is considered. It is shown that, as the thickness of VEM layer vanishes, the results become a simple layer beam's that.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.17-24
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• 2004

This paper established the dynamic model of a flexible Timoshenko beam with geometrical nonlinearities subject to large overall motions by using the finite element method. The equations of motion are derived by using Hamilton principle based on expressing the kinetic and potential energies of the flexible beam in terms of generalized coordinates. The nonlinear constraint equations are adjoined to the system equations of motion by using Lagrange multipliers.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.675-680
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• 2006

This paper deals with the flexural free vibrations of strip foundations. Based on dynamic equilibrium equations of a beam element resting on Winkler foundation, differential equations governing free vibration of strip foundation are derived, in which effects of rotatory inertia and shear deformation are included. For obtaining the natural frequencies, differential equations are solved by numerical methods. As the numerical results, relationships between natural frequencies and various strip parameters are obtained and presented in Tables and Figures.