T.Y. Wu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.82, No.2, pp. 83-112, 2011, DOI:10.32604/cmes.2011.082.083

Abstract In this work nonlinear analysis of axi-symmetric solid using vector mechanics is performed, in which a triangular solid unit developed in compliance with the concept of vector form analysis is proposed. The vector form analysis uses point value description (rather than function) to describe motion and configuration of solid, which has governing equation directly formulated with respect to each mass point (particle). The point value description includes particles allocation for configuration and defining path elements for particle motion. In addition, constitutive conditions are properly defined to complete the formulation. The constitutive conditions linking the mass points in deformable solids are… More >

A. Gakwaya¹, H. Sharifi², M. Guillot¹, M. Souli³, F. Erchiqui⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.3, pp. 209-266, 2011, DOI:10.3970/cmes.2011.073.209

Abstract A mechanical computer aided design and engineering system can be used to reduce the design-to-manufacture cycle time in metal forming process. Such a system could be built upon a solid modeling geometry engine and an efficient finite element (FE) solver. The maintenance of a high-quality mesh throughout the analysis is an essential feature of an efficient finite element simulation of large strain metal forming problems. In this paper, a mesh adaptation technique employing the Arbitrary Lagrangian-Eulerian formulation (ALE) is applied to some industrial metal forming problems. An ACIS boundary representation of the solid model is employed. This type of representation… More >

P.D.Gosling^1,2, L. Zhang²

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.3, pp. 203-252, 2011, DOI:10.3970/cmes.2011.071.203

Abstract The analysis of a continuum membrane by means of a discrete network of cables or bars is an efficient and readily tractable approach to the solution of a complex mechanics problem. However, is so doing, compromises are made in the quality of the approximation of the strain field. It is shown in this paper that the original form of the cable-analogy continuum triangle formulation is degraded by an inherent assumption of small strains in the underlying equations, in which the term ßmall" is shown to be "negligibly small". A revised version of this formulation is proposed in which a modification… 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 >

S. Hartmann¹, R. Weyler², J. Oliver¹, J.C. Cante², J.A. Hernández¹

CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.3, pp. 211-270, 2010, DOI:10.3970/cmes.2010.055.211

Abstract This work describes a three-dimensional contact domain method for large deformation frictionless contact problems. Theoretical basis and numerical aspects of this specific contact method are given in [Oliver, Hartmann, Cante, Weyler and Hernández (2009)] and [Hartmann, Oliver, Weyler, Cante and Hernández (2009)] for two-dimensional, large deformation frictional contact problems. In this method, in contrast to many other contact formulations, the necessary contact constraints are formulated on a so-called contact domain, which can be interpreted as a fictive intermediate region connecting the potential contact surfaces of the deformable bodies. This contact domain has the same dimension as the contacting bodies. It… More >

Z. T. Ma¹, X. Zhang^1,2, P. Huang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.1, pp. 61-88, 2010, DOI:10.3970/cmes.2010.055.061

Abstract The Material Point Method (MPM) is more expensive in terms of storage than other methods, as MPM makes use of both mesh and particle data. Therefore, it is critical to develop an efficient MPM framework for engineering applications, such as impact and explosive simulations. This paper presents a new architecture for MPM computer code, developed using object-oriented design, which enables MPM analysis of a mass of grains, large deformation, high strain rates and complex material behavior. It is flexible, extendible, and easily modified for a variety of MPM analysis procedures. An MPM scheme combining contact algorithm with USF, USL and… 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 >