http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
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.
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.
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.
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.