Free vibrations of inclined arches using finite elements

Somchai Chucheepsakul,WasurootSaetiew 국제구조공학회 2002 Structural Engineering and Mechanics, An Int'l Jou Vol.14 No.6

Large deflection analysis of orthotropic, elliptic membranes

Somchai Chucheepsakul,Sakdirat Kaewunruen,Apiwat Suwanarat 국제구조공학회 2009 Structural Engineering and Mechanics, An Int'l Jou Vol.32 No.1

Applications of membrane mechanisms are widely found in nano-devices and nano-sensor technologies nowadays. An alternative approach for large deflection analysis of the orthotropic, elliptic membranes . subject to gravitational, uniform pressures often found in nano-sensors . is described in this paper. The material properties of membranes are assumed to be orthogonally isotropic and linearly elastic, while the principal directions of elasticity are parallel to the coordinate axes. Formulating the potential energy functional of the orthotropic, elliptic membranes involves the strain energy that is attributed to inplane stress resultant and the potential energy due to applied pressures. In the solution method, Rayleigh-Ritz method can be used successfully to minimize the resulting total potential energy generated. The set of equilibrium equations was solved subsequently by Newton-Raphson. The unparalleled model formulation capable of analyzing the large deflections of both circular and elliptic membranes is verified by making numerical comparisons with existing results of circular membranes as well as finite element solutions. The results are found in excellent agreements at all cases. Then, the parametric investigations are given to delineate the impacts of the aspect ratios and orthotropic elasticity on large static tensions and deformations of the orthotropic, elliptic membranes.

Large deflection analysis of orthotropic, elliptic membranes

Somchai Chucheepsakul,Sakdirat Kaewunruen,Apiwat Suwanarat 국제구조공학회 2009 Structural Engineering and Mechanics, An Int'l Jou Vol.31 No.6

Applications of membrane mechanisms are widely found in nano-devices and nano-sensor technologies nowadays. An alternative approach for large deflection analysis of the orthotropic, elliptic membranes – subject to gravitational, uniform pressures often found in nano-sensors – is described in this paper. The material properties of membranes are assumed to be orthogonally isotropic and linearly elastic, while the principal directions of elasticity are parallel to the coordinate axes. Formulating the potential energy functional of the orthotropic, elliptic membranes involves the strain energy that is attributed to inplane stress resultant and the potential energy due to applied pressures. In the solution method, Rayleigh-Ritz method can be used successfully to minimize the resulting total potential energy generated. The set of equilibrium equations was solved subsequently by Newton-Raphson. The unparalleled model formulation capable of analyzing the large deflections of both circular and elliptic membranes is verified by making numerical comparisons with existing results of circular membranes as well as finite element solutions. The results are found in excellent agreements at all cases. Then, the parametric investigations are given to delineate the impacts of the aspect ratios and orthotropic elasticity on large static tensions and deformations of the orthotropic, elliptic membranes.

Large deflection analysis of orthotropic, elliptic membranes

Chucheepsakul, Somchai,Kaewunruen, Sakdirat,Suwanarat, Apiwat Techno-Press 2009 Structural Engineering and Mechanics, An Int'l Jou Vol.31 No.6

Applications of membrane mechanisms are widely found in nano-devices and nano-sensor technologies nowadays. An alternative approach for large deflection analysis of the orthotropic, elliptic membranes - subject to gravitational, uniform pressures often found in nano-sensors - is described in this paper. The material properties of membranes are assumed to be orthogonally isotropic and linearly elastic, while the principal directions of elasticity are parallel to the coordinate axes. Formulating the potential energy functional of the orthotropic, elliptic membranes involves the strain energy that is attributed to inplane stress resultant and the potential energy due to applied pressures. In the solution method, Rayleigh-Ritz method can be used successfully to minimize the resulting total potential energy generated. The set of equilibrium equations was solved subsequently by Newton-Raphson. The unparalleled model formulation capable of analyzing the large deflections of both circular and elliptic membranes is verified by making numerical comparisons with existing results of circular membranes as well as finite element solutions. The results are found in excellent agreements at all cases. Then, the parametric investigations are given to delineate the impacts of the aspect ratios and orthotropic elasticity on large static tensions and deformations of the orthotropic, elliptic membranes.

Effect of axial stretching on large amplitude free vibration of a suspended cable

Chucheepsakul, Somchai,Wongsa, Sanit Techno-Press 2001 Structural Engineering and Mechanics, An Int'l Jou Vol.11 No.2

This paper presents the effect of axial stretching on large amplitude free vibration of an extensible suspended cable supported at the same level. The model formulation developed in this study is based on the virtual work-energy functional of cables which involves strain energy due to axial stretching and work done by external forces. The difference in the Euler equations between equilibrium and motion states is considered. The resulting equations govern the horizontal and vertical motion of the cables, and are coupled and highly nonlinear. The solution for the nonlinear static equilibrium configuration is determined by the shooting method while the solution for the large amplitude free vibration is obtained by using the second-order central finite difference scheme with time integration. Numerical examples are given to demonstrate the vibration behaviour of extensible suspended cables.

Free vibrations of inclined arches using finite elements

Chucheepsakul, Somchai,Saetiew, Wasuroot Techno-Press 2002 Structural Engineering and Mechanics, An Int'l Jou Vol.13 No.6

This paper presents a finite element approach for determining the natural frequencies for planar inclined arches of various shapes vibrating in three-dimensional space. The profile of inclined arches, represented by undeformed centriodal axis of cross-section, is defined by the equation of plane curves expressed in the rectangular coordinates which are : circular, parabolic, sine, elliptic, and catenary shapes. In free vibration state, the arch is slightly displaced from its undeformed position. The linear relationship between curvature-torsion and axial strain is expressed in terms of the displacements in three-dimensional space. The finite element discretization along the span length is used rather than the total are length. Numerical results for arches of various shapes are given and they are in good agreement with those reported in literature. The natural frequency parameters and mode shapes are reported as functions of two nondimensional parameters: the span to cord length ratio (e) and the rise to cord length ratio (f).

Exact solutions of variable-arc-length elasticas under moment gradient

Chucheepsakul, Somchai,Thepphitak, Geeraphong,Wang, Chien Ming Techno-Press 1997 Structural Engineering and Mechanics, An Int'l Jou Vol.5 No.5

This paper deals with the bending problem of a variable-are-length elastica under moment gradient. The variable are-length arises from the fact that one end of the elastica is hinged while the other end portion is allowed to slide on a frictionless support that is fixed at a given horizontal distance from the hinged end. Based on the elastica theory, exact closed-form solution in the form of elliptic integrals are derived. The bending results show that there exists a maximum or a critical moment for given moment gradient parameters; whereby if the applied moment is less than this critical value, two equilibrium configurations are possible. One of them is stable while the other is unstable because a small disturbance will lead to beam motion.

Large deflections of spatial variable-arc-length elastica under terminal forces

Phungpaingam, Boonchai,Athisakul, Chainarong,Chucheepsakul, Somchai Techno-Press 2009 Structural Engineering and Mechanics, An Int'l Jou Vol.32 No.4

This paper aims to study the large deflections of variable-arc-length elastica subjected to the terminal forces (e.g., axial force and torque). Based on Kirchhoff's rod theory and with help of Euler parameters, the set of nonlinear governing differential equations which free from the effect of singularity are established together with boundary conditions. The system of nonlinear differential equations is solved by using the shooting method with high accuracy integrator, seventh-eighth order Runge-Kutta with adaptive step-size scheme. The error norm of end conditions is minimized within the prescribed tolerance ($10^{-5}$). The behavior of VAL elastica is studied by two processes. One is obtained by applying slackening first. After that keeping the slackening as a constant and then the twist angle is varied in subsequent order. The other process is performed by reversing the sequence of loading in the first process. The results are interpreted by observing the load-deflection diagram and the stability properties are predicted via fold rule. From the results, there are many interesting aspects such as snap-through phenomenon, secondary bifurcation point, loop formation, equilibrium configurations and effect of variable-arc-length to behavior of elastica.

Large deflections of spatial variable-arc-length elastica under terminal forces

Boonchai Phungpaingam,Chainarong Athisakul,Somchai Chucheepsakul 국제구조공학회 2009 Structural Engineering and Mechanics, An Int'l Jou Vol.32 No.4

This paper aims to study the large deflections of variable-arc-length elastica subjected to the terminal forces (e.g., axial force and torque). Based on Kirchhoff’s rod theory and with help of Euler parameters, the set of nonlinear governing differential equations which free from the effect of singularity are established together with boundary conditions. The system of nonlinear differential equations is solved by using the shooting method with high accuracy integrator, seventh-eighth order Runge-Kutta with adaptive step-size scheme. The error norm of end conditions is minimized within the prescribed tolerance (10.5). The behavior of VAL elastica is studied by two processes. One is obtained by applying slackening first. After that keeping the slackening as a constant and then the twist angle is varied in subsequent order. The other process is performed by reversing the sequence of loading in the first process. The results are interpreted by observing the load-deflection diagram and the stability properties are predicted via fold rule. From the results, there are many interesting aspects such as snap-through phenomenon, secondary bifurcation point, loop formation, equilibrium configurations and effect of variable-arc-length to behavior of elastica.

Flexural Responses of Concrete Slab over Flexible Girders through FEA-Based Parametric Evaluation

Sudathip Tangwongchai,Naveed Anwar,Somchai Chucheepsakul 대한토목학회 2011 KSCE JOURNAL OF CIVIL ENGINEERING Vol.15 No.6

The determination of flexural responses in a concrete slab over flexible steel girder, forming a composite deck has been a timeconsuming subject for the design engineers. The existing provisions of the design standards such as AASHTO or analytical solutions based on local bending or plate theory usually ignore some significant parameters affecting the deck response, such as girder flexibility, number of loaded traffic lanes and ratio between deck width and girder span. This may lead to unrealistic prediction of bridge flexural responses used in the slab design practice. Although it is well known that finite element analysis is very versatile for structural analysis, very few studies have been reported dealing with explicit determination of deck slab response. The present study investigates the transverse negative bending moment of the slab cast over a number of steel girders, subjected to traffic loads, using verified composite Shell-Frame and Plate-Frame Models. The evaluation of such response is carried out through an extensive parametric study focusing on the effect of girder flexibility due to patterns of moving loads. Based on the numerical results, empirical relationships are proposed to determine the maximum slab moments anywhere along the girder span. The application of these relationships is then compared with other references. The suggested relationships seem to give more realistic and economical values of the considered transverse slab bending moment for a wide range of deck proportions.