Correlation between beam on Winkler-Pasternak foundation and beam on elastic substrate medium with inclusion of microstructure and surface effects

Suchart Limkatanyu,Paitoon Ponbunyanon,Woraphot Prachasaree,Kittisak Kuntiyawichai,권민호 대한기계학회 2014 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.28 No.9

A novel beam-elastic substrate element with inclusion of microstructure and surface energy effects is proposed in this paper. Themodified couple stress theory is employed to account for the microstructure-dependent effect of the beam bulk material while Gurtin-Murdoch surface theory is used to capture the surface energy-dependent size effect. Interaction mechanism between the beam and thesurrounding substrate medium is represented by the Winkler foundation model. The governing differential equilibrium and compatibilityequations of the beam-elastic substrate system are consistently derived based on virtual displacement and virtual force principles, respectively. Both essential and natural boundary conditions of the system are also obtained. Two modified Tonti’s diagrams are presented toprovide the big picture of both displacement-based and force-based formulations of the system. Due to similarity between the currentproblem and the one related to the beam on Winkler-Pasternak foundation, the so-called “natural” beam-Winkler-Pasternak foundationelement coined by the authors is employed to perform two numerical simulations to study the characteristics and behaviors of a beamsubstratesystem with inclusion of microstructure and surface effects.

Nonlinear Winkler-based Beam Element with Improved Displacement Shape Functions

Suchart Limkatanyu,Kittisak Kuntiyawichai,Enrico Spacone,권민호 대한토목학회 2013 KSCE JOURNAL OF CIVIL ENGINEERING Vol.17 No.1

This paper presents a Winkler-based beam element capable of representing the nonlinear interaction mechanics between the beam and the foundation. The element is derived based on a displacement-based formulation using improved displacement shape functions. The improved displacement shape functions are analytically derived based on the homogeneous solution to the governing differential equilibrium equation of the problem, thus enhancing the model accuracy. An iterative technique is used to determine the length-scale parameter needed in evaluating the displacement shape functions. Two numerical examples are used to verify the accuracy and the efficiency of the proposed Winkler-based beam model.

Natural stiffness matrix for beams on Winkler foundation: exact force-based derivation

Suchart Limkatanyu,Kittisak Kuntiyawichai,Enrico Spacone,권민호 국제구조공학회 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.42 No.1

This paper presents an alternative way to derive the exact element stiffness matrix for a beam on Winkler foundation and the fixed-end force vector due to a linearly distributed load. The element flexibility matrix is derived first and forms the core of the exact element stiffness matrix. The governing differential compatibility of the problem is derived using the virtual force principle and solved to obtain the exact moment interpolation functions. The matrix virtual force equation is employed to obtain the exact element flexibility matrix using the exact moment interpolation functions. The so-called “natural” element stiffness matrix is obtained by inverting the exact element flexibility matrix. Two numerical examples are used to verify the accuracy and the efficiency of the natural beam element on Winkler foundation.

Natural stiffness matrix for beams on Winkler foundation: exact force-based derivation

Limkatanyu, Suchart,Kuntiyawichai, Kittisak,Spacone, Enrico,Kwon, Minho Techno-Press 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.42 No.1

This paper presents an alternative way to derive the exact element stiffness matrix for a beam on Winkler foundation and the fixed-end force vector due to a linearly distributed load. The element flexibility matrix is derived first and forms the core of the exact element stiffness matrix. The governing differential compatibility of the problem is derived using the virtual force principle and solved to obtain the exact moment interpolation functions. The matrix virtual force equation is employed to obtain the exact element flexibility matrix using the exact moment interpolation functions. The so-called "natural" element stiffness matrix is obtained by inverting the exact element flexibility matrix. Two numerical examples are used to verify the accuracy and the efficiency of the natural beam element on Winkler foundation.

Contact interface fiber section element: shallow foundation modeling

Limkatanyu, Suchart,Kwon, Minho,Prachasaree, Woraphot,Chaiviriyawong, Passagorn Techno-Press 2012 Geomechanics & engineering Vol.4 No.3

With recent growing interests in the Performance-Based Seismic Design and Assessment Methodology, more realistic modeling of a structural system is deemed essential in analyzing, designing, and evaluating both newly constructed and existing buildings under seismic events. Consequently, a shallow foundation element becomes an essential constituent in the implementation of this seismic design and assessment methodology. In this paper, a contact interface fiber section element is presented for use in modeling soil-shallow foundation systems. The assumption of a rigid footing on a Winkler-based soil rests simply on the Euler-Bernoulli's hypothesis on sectional kinematics. Fiber section discretization is employed to represent the contact interface sectional response. The hyperbolic function provides an adequate means of representing the stress-deformation behavior of each soil fiber. The element is simple but efficient in representing salient features of the soil-shallow foundation system (sliding, settling, and rocking). Two experimental results from centrifuge-scale and full-scale cyclic loading tests on shallow foundations are used to illustrate the model characteristics and verify the accuracy of the model. Based on this comprehensive model validation, it is observed that the model performs quite satisfactorily. It resembles reasonably well the experimental results in terms of moment, shear, settlement, and rotation demands. The hysteretic behavior of moment-rotation responses and the rotation-settlement feature are also captured well by the model.

Total Lagrangian Formulation of 2D Bar Element using Vectorial Kinematical Description

Suchart Limkatanyu,Woraphot Prachasaree,Griengsak Kaewkulchai,권민호 대한토목학회 2013 KSCE Journal of Civil Engineering Vol.17 No.6

Based on the total Lagrangian kinematical description, a geometrically nonlinear bar element is developed for large-displacement and post-buckling analyses of plane truss structures. Firstly, the vectorial form is used to explicitly describe the element kinematics and element strain in terms of element nodal displacements, thus eliminating the need of shape functions as required in a standard finite element formulation. Secondly, the virtual displacement principle is employed to represent the element equilibrium in the integral form. Due to the nonlinear nature of the system, the directional derivative operator is used to linearize the virtual displacement equation, resulting in an incremental form of equilibrium equations. Thirdly, the generalized displacement control method is adopted in obtaining the incremental solution of problems. Finally, several structures exhibiting different types of critical points are analyzed to verify the element accuracy and assess the ability of solution algorithm to trace nonlinear responses. In this paper, the MATLAB programming language is used for coding and in-house software development.

Nonlinear Frame Element with Shear– Flexure Interaction for Seismic Analysis of Non-Ductile Reinforced Concrete Columns

Worathep Sae-Long,Suchart Limkatanyu,Woraphot Prachasaree,Suksun Horpibulsuk,Pattamad Panedpojaman 한국콘크리트학회 2019 International Journal of Concrete Structures and M Vol.13 No.5

This paper presents and emphasizes the essence of inclusion of shear response and shear–flexural interaction in the investigation of reinforced concrete (RC) columns characterized by light and inadequately (substandard) detailed transverse reinforcement. This column type commonly exists in old-constructed RC frame buildings before the regulation of modern seismic codes. A stiffness-based RC frame element with shear–flexure interaction is formulated within the framework of Timoshenko beam kinematics assumption. Linked displacement interpolation functions are employed to remedy the problematic shear-locking phenomenon. The axial and flexural actions are interacted via the fiber-section model while shear-strength deterioration with inelastic flexural deformations is accounted for within the framework of the UCSD shear-strength model. The numerical procedure for shear–flexure interaction is modified from the Mergos–Kappos procedure. The proposed element is simple, computationally efficient and able to describe several salient features of RC columns with substandard detailed transverse reinforcement, including gradual spread inelasticity, shear–flexure coupling effects, and shear-strength deterioration with increasing curvature ductility. Three correlation studies are conducted to examine the model accuracy and its capability to predict the rather complex responses of non-ductile RC columns. Comparison with conventional flexural frame element is also presented to emphasize the essence of inclusion of shear response and shear–flexure interaction.

Temperature effect on multi-ionic species diffusion in saturated concrete

Nattapong Damrongwiriyanupap,Linyuan Li,Suchart Limkatanyu,Yunping Xi 사단법인 한국계산역학회 2014 Computers and Concrete, An International Journal Vol.13 No.2

This study presents the mathematical model for predicting chloride penetration into saturated concrete under non-isothermal condition. The model considers not only diffusion mechanism but also migration process of chloride ions and other chemical species in concrete pore solution such as sodium, potassium, and hydroxyl ions. The coupled multi-ionic transport in concrete is described by the Nernst-Planck equation associated with electro-neutrality condition. The coupling parameter taken into account the effect of temperature on ion diffusion obtained from available test data is proposed and explicitly incorporated in the governing equations. The coupled transport equations are solved using the finite element method. The numerical results are validated with available experimental data and the comparison shows a good agreement.

Bar와 Beam 구조물의 기본적인 유한요소 모델의 수치해석

류용희 ( Yong Hee Ryu ),주부석 ( Bu Seog Ju ),정우영 ( Woo Young Jung ),( Suchart Limkatanyu ) 한국복합신소재구조학회 2013 복합신소재구조학회논문집 Vol.4 No.1

The finite element analysis (FEA) is a numerical technique to find solutions of field problems. A field problem is approximated by differential equations or integral expressions. In a finite element, the field quantity is allowed to have a simple spatial variation in terms of linear or polynomial functions. This paper represents a review and an accuracy-study of the finite element method comparing the FEA results with the exact solution. The exact solutions were calculated by solid mechanics and FEA using matrix stiffness method. For this study, simple bar and cantilever models were considered to evaluate four types of basic elements - constant strain triangle (CST), linear strain triangle (LST), bi-linear-rectangle(Q4),and quadratic-rectangle(Q8). The bar model was subjected to uniaxial loading whereas in case of the cantilever model moment loading was used. In the uniaxial loading case, all basic element results of the displacement and stress in x-direction agreed well with the exact solutions. In the moment loading case, the displacement in y-direction using LST and Q8 elements were acceptable compared to the exact solution, but CST and Q4 elements had to be improved by the mesh refinement.

Bar와 Beam 구조물의 기본적인 유한요소 모델의 수치해석

Ryu, Yong-Hee,Ju, Bu-Seog,Jung, Woo-Young,Suchart Limkatanyu 한국복합신소재구조학회 2013 복합신소재구조학회논문집 Vol.4 No.1

The finite element analysis (FEA) is a numerical technique to find solutions of field problems. A field problem is approximated by differential equations or integral expressions. In a finite element, the field quantity is allowed to have a simple spatial variation in terms of linear or polynomial functions. This paper represents a review and an accuracy-study of the finite element method comparing the FEA results with the exact solution. The exact solutions were calculated by solid mechanics and FEA using matrix stiffness method. For this study, simple bar and cantilever models were considered to evaluate four types of basic elements - constant strain triangle (CST), linear strain triangle (LST), bi-linear-rectangle(Q4),and quadratic-rectangle(Q8). The bar model was subjected to uniaxial loading whereas in case of the cantilever model moment loading was used. In the uniaxial loading case, all basic element results of the displacement and stress in x-direction agreed well with the exact solutions. In the moment loading case, the displacement in y-direction using LST and Q8 elements were acceptable compared to the exact solution, but CST and Q4 elements had to be improved by the mesh refinement.