Amel A. Alaidrous^*

CMC-Computers, Materials & Continua, Vol.67, No.3, pp. 2971-2988, 2021, DOI:10.32604/cmc.2021.015159

Abstract In this paper, we study the water-wave flow under a floating body of an incident wave in a fluid. This model simulates the phenomenon of waves abording a floating ship in a vast ocean. The same model, also simulates the phenomenon of fluid-structure interaction of a large ice sheet in waves. According to this method. We divide the region of the problem into three subregions. Solutions, satisfying the equation in the fluid mass and a part of the boundary conditions in each subregion, are given. We obtain such solutions as infinite series including unknown coefficients. We consider a limited number… More >

Victor A. Eremeyev

The International Conference on Computational & Experimental Engineering and Sciences, Vol.19, No.3, pp. 81-82, 2011, DOI:10.3970/icces.2011.019.081

Abstract The aim of this work is to discuss the nonlinear theory of shells made of material undergoing phase transitions (PT). The interest to mechanics and thermodynamics of thin-walled structures with PT is motivated by the recent investigations of thin martensitic films and biological membranes. Here we present statements of the boundary-value problems of shells and plates with PT within the dynamically and kinematically exact theory of shells. In this shell theory the translation and rotation fields are the kinematically independent variables. The theoretical model is illustrated by the examples of thin circular cylindrical shell and circular plate made of two-phase… More >

Wojciech Pietraszkiewicz

The International Conference on Computational & Experimental Engineering and Sciences, Vol.16, No.3, pp. 89-90, 2011, DOI:10.3970/icces.2011.016.089

Abstract Wei-zhang Chien (1944) derived the equilibrium equations and the compatibility conditions of the nonlinear theory of thin, isotropic elastic shells entirely in terms of the surface stress and strain measures associated with the shell base surface. This allowed Him to divide the complex boundary value problem (BVP) of nonlinear shell analysis into two disjoint and supposedly simpler steps: I) finding the surface stress and strain measures, and II) establishing displacements from already known surfacestrainmeasures. In the present paper some achievements of this formulation obtained during the last 66 years are reviewed, with special account of the results obtained by the… More >

W. Pietraszkiewicz¹

CMES-Computer Modeling in Engineering & Sciences, Vol.70, No.2, pp. 153-190, 2010, DOI:10.3970/cmes.2010.070.153

Abstract Chien Wei-Zhang (1944) derived three equilibrium equations and three compatibility conditions of the nonlinear theory of thin, isotropic elastic shells entirely in terms of the surface stress and strain measures associated with the shell base surface. This allowed Him to divide the complex boundary value problem (BVP) of nonlinear shell analysis into two disjoint and supposedly simpler steps: I) finding the surface stress and strain measures from the intrinsic BVP, and II) establishing position in space of the deformed base surface from already known surface strain measures. In the present paper some achievements of this formulation obtained during the last… More >

Y.C. Cai¹, S.N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.3, pp. 249-274, 2012, DOI:10.3970/cmes.2012.083.249

Abstract This paper presents a very simple finite element method for geometrically nonlinear large rotation analyses of plate/shell structures comprising of thin members. A fully nonlinear theory of deformation is employed in the updated Lagrangian reference frame of each plate element, to account for bending, stretching and torsion of each element. An assumed displacement approach, based on the Discrete Kirchhoff Theory (DKT) over each element, is employed to derive an explicit expression for the (18x18) symmetric tangent stiffness matrix of the plate element in the co-rotational reference frame. The finite rotation of the updated Lagrangian reference frame relative to a globally… More >

Y.C. Cai^1,2, J.K. Paik³, S.N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.61, No.3, pp. 273-312, 2010, DOI:10.3970/cmes.2010.061.273

Abstract This paper presents an elementary finite element method for geometrically nonlinear large rotation analyses of built-up plate/shell structures comprising of thin members. The tangent stiffness matrix of the element in the updated Lagrangian co-rotational reference frame is developed, based on the von Karman nonlinear theory of plates, and the Reissner variational principle, allowing for unsymmetric stresses and drilling rotations, useful in the analysis of built-up plate and shell structure. The finite rotation of the co-rotational reference frame relative to a globally fixed Cartesian frame, is simply determined from the finite displacement vectors of the nodes of the element in the… More >

Y.C. Cai^1,2, J.K. Paik³, S.N. Atluri⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.1, pp. 75-108, 2010, DOI:10.3970/cmes.2010.058.075

Abstract This paper presents a new shear flexible beam/rod element for large deformation analyses of space-frame structures comprising of thin or thick members, based on the Reissner variational principle and a von Karman type nonlinear theory of deformation in the co-rotational reference frame of the present beam element. The C0continuous trial functions for transverse rotations in two independent directions are used over each element, to derive an explicit expression for the (16x16)symmetrictangent stiffness matrix of the beam element in the co-rotational reference frame. When compared to the primal approach wherein C1continuous trial functions for transverse displacements over each element are necessary,… More >

H.H. Zhu¹, Y.C. Cai^1,2, J.K. Paik³, S.N. Atluri⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.57, No.2, pp. 175-204, 2010, DOI:10.3970/cmes.2010.057.175

Abstract This paper presents a new shear flexible beam/rod element for large deformation analyses of space-frame structures, comprising of thin or thick beams. The formulations remain uniformly valid for thick or thin beams, without using any numerical expediencies such as selective reduced integrations, etc. A von Karman type nonlinear theory of deformation is employed in the co-rotational reference frame of the present beam element, to account for bending, stretching, torsion and shearing of each element. Transverse shear strains in two independant directions are introduced as additional variables, in order to eliminate the shear locking phenomenon. An assumed displacement approach is used… More >

Yongchang Cai^1,2, J.K. Paik³, Satya N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.3, pp. 335-368, 2009, DOI:10.3970/cmes.2009.054.335

Abstract This paper presents a simple finite element method, based on assumed moments and rotations, for geometrically nonlinear large rotation analyses of space frames consisting of members of arbitrary cross-section. A von Karman type nonlinear theory of deformation is employed in the updated Lagrangian co-rotational reference frame of each beam element, to account for bending, stretching, and torsion of each element. The Reissner variational principle is used in the updated Lagrangian co-rotational reference frame, to derive an explicit expression for the (12x12)symmetrictangent stiffness matrix of the beam element in the co-rotational reference frame. The explicit expression for the finite rotation of… More >

Yongchang Cai^1,2, J.K. Paik³, Satya N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.2, pp. 123-152, 2009, DOI:10.3970/cmes.2009.053.123

Abstract This paper presents a simple finite element method, based on simple mechanics and physical clarity, for geometrically nonlinear large rotation analyses of space frames consisting of members of arbitrary cross-section. A co-rotational reference frame, involving the axes of each finitely rotated beam finite-element, is used as the Updated Lagrangian reference frame for the respective element. A von Karman type nonlinear theory of deformation is employed in the co-rotational reference frame of each beam element, to account for bending, stretching, and torsion of each element. An assumed displacement approach is used to derive an explicit expression for the (12x12)symmetrictangent stiffness matrix… More >