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Present Formulation (present + formulation)
Selected AbstractsAn efficient co-rotational formulation for curved triangular shell elementINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2007Zhongxue Li Abstract A 6-node curved triangular shell element formulation based on a co-rotational framework is proposed to solve large-displacement and large-rotation problems, in which part of the rigid-body translations and all rigid-body rotations in the global co-ordinate system are excluded in calculating the element strain energy. Thus, an element-independent formulation is achieved. Besides three translational displacement variables, two components of the mid-surface normal vector at each node are defined as vectorial rotational variables; these two additional variables render all nodal variables additive in an incremental solution procedure. To alleviate the membrane and shear locking phenomena, the membrane strains and the out-of-plane shear strains are replaced with assumed strains in calculating the element strain energy. The strategy used in the mixed interpolation of tensorial components approach is employed in defining the assumed strains. The internal force vector and the element tangent stiffness matrix are obtained from calculating directly the first derivative and second derivative of the element strain energy with respect to the nodal variables, respectively. Different from most other existing co-rotational element formulations, all nodal variables in the present curved triangular shell formulation are commutative in calculating the second derivative of the strain energy; as a result, the element tangent stiffness matrix is symmetric and is updated by using the total values of the nodal variables in an incremental solution procedure. Such update procedure is advantageous in solving dynamic problems. Finally, several elastic plate and shell problems are solved to demonstrate the reliability, efficiency, and convergence of the present formulation. Copyright © 2007 John Wiley & Sons, Ltd. [source] Multiscale Galerkin method using interpolation wavelets for two-dimensional elliptic problems in general domainsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2004Gang-Won Jang Abstract One major hurdle in developing an efficient wavelet-based numerical method is the difficulty in the treatment of general boundaries bounding two- or three-dimensional domains. The objective of this investigation is to develop an adaptive multiscale wavelet-based numerical method which can handle general boundary conditions along curved boundaries. The multiscale analysis is achieved in a multi-resolution setting by employing hat interpolation wavelets in the frame of a fictitious domain method. No penalty term or the Lagrange multiplier need to be used in the present formulation. The validity of the proposed method and the effectiveness of the multiscale adaptive scheme are demonstrated by numerical examples dealing with the Dirichlet and Neumann boundary-value problems in quadrilateral and quarter circular domains. Copyright © 2003 John Wiley & Sons, Ltd. [source] Enrichment of enhanced assumed strain approximations for representing strong discontinuities: addressing volumetric incompressibility and the discontinuous patch testINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004J. E. Dolbow Abstract We present a geometrically non-linear assumed strain method that allows for the presence of arbitrary, intra-finite element discontinuities in the deformation map. Special attention is placed on the coarse-mesh accuracy of these methods and their ability to avoid mesh locking in the incompressible limit. Given an underlying mesh and an arbitrary failure surface, we first construct an enriched approximation for the deformation map with the non-linear analogue of the extended finite element method (X-FEM). With regard to the richer space of functions spanned by the gradient of the enriched approximation, we then adopt a broader interpretation of variational consistency for the construction of the enhanced strain. In particular, in those elements intersected by the failure surface, we construct enhanced strain approximations which are orthogonal to piecewise-constant stress fields. Contrast is drawn with existing strong discontinuity approaches where the enhanced strain variations in localized elements were constructed to be orthogonal to constant nominal stress fields. Importantly, the present formulation gives rise to a symmetric tangent stiffness matrix, even in localized elements. The present modification also allows for the satisfaction of a discontinuous patch test, wherein two different constant stress fields (on each side of the failure surface) lie in the solution space. We demonstrate how the proposed modifications eliminate spurious stress oscillations along the failure surface, particularly for nearly incompressible material response. Additional numerical examples are provided to illustrate the efficacy of the modified method for problems in hyperelastic fracture mechanics. Copyright © 2003 John Wiley & Sons, Ltd. [source] Non-local dispersive model for wave propagation in heterogeneous media: one-dimensional caseINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2002Jacob Fish Abstract Non-local dispersive model for wave propagation in heterogeneous media is derived from the higher-order mathematical homogenization theory with multiple spatial and temporal scales. In addition to the usual space,time co-ordinates, a fast spatial scale and a slow temporal scale are introduced to account for rapid spatial fluctuations of material properties as well as to capture the long-term behaviour of the homogenized solution. By combining various order homogenized equations of motion the slow time dependence is eliminated giving rise to the fourth-order differential equation, also known as a ,bad' Boussinesq problem. Regularization procedures are then introduced to construct the so-called ,good' Boussinesq problem, where the need for C1 continuity is eliminated. Numerical examples are presented to validate the present formulation. Copyright © 2002 John Wiley & Sons, Ltd. [source] A basic thin shell triangle with only translational DOFs for large strain plasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2001Fernando G. Flores Abstract A simple finite element triangle for thin shell analysis is presented. It has only nine translational degrees of freedom and is based on a total Lagrangian formulation. Large strain plasticity is considered using a logarithmic strain,stress pair. A plane stress isotropic behaviour with an additive decomposition of elastic and plastic strains is assumed. A hyperelastic law is considered for the elastic part while for the plastic part a von Mises yield function with non-linear isotropic hardening is adopted. The element is an extension of a previous similar rotation-free triangle element based upon an updated Lagrangian formulation with hypoelastic constitutive law. The element termed BST (for basic shell triangle) has been implemented in an explicit (hydro-) code adequate to simulate sheet-stamping processes and in an implicit static/dynamic code. Several examples are shown to assess the performance of the present formulation. Copyright © 2001 John Wiley & Sons, Ltd. [source] A robust surface-integral-equation formulation for conductive mediaMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 2 2005Yun-Hui Chu Abstract A novel surface-integral-equation (SIE) formulation is proposed by tuning the weighting coefficients for the external- and internal-region integral equations. Without increasing the computational cost, the present formulation significantly enlarges the solvable skin-depth range. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 46: 109,114, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20916 [source] Numerical integration of differential-algebraic equations with mixed holonomic and control constraintsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Mahmud Quasem The present work aims at the incorporation of control (or servo) constraints into finite,dimensional mechanical systems subject to holonomic constraints. In particular, we focus on underactuated systems, defined as systems in which the number of degrees of freedom exceeds the number of inputs. The corresponding equations of motion can be written in the form of differential,algebraic equations (DAEs) with a mixed set of holonomic and control constraints. Apart from closed,loop multibody systems, the present formulation accommodates the so,called rotationless formulation of multibody dynamics. To this end, we apply a specific projection method to the DAEs in terms of redundant coordinates. A similar projection approach has been previously developed in the framework of generalized coordinates by Blajer & Ko,odziejczyk [1]. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A Finite Element Approach for the Simulation of Quasi-Brittle FracturePROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005Oliver Hilgert In the context of a strong discontinuity approach, we propose a finite element formulation with an embedded displacement discontinuity. The basic assumption of the proposed approach is the additive split of the total displacement field in a continuous and a discontinuous part. An arbitrary crack splits the linear triangular finite element into two parts, namely a triangular and a quadrilateral part. The discontinuous part of the displacement field in the quadrilateral portion is approximated using linear shape functions. For these purposes, the quadrilateral portion is divided into two triangular parts which is in this way similar to the approach proposed in [5]. In contrast, the discretisation is different compared to formulations proposed in [1] and [3], where the discontinuous part of the displacement field is approximated using bilinear shape functions. The basic theory of the underlying finite element formulation and a cohesive interface model to simulate brittle fracture are presented. By means of representative numerical examples differences and similarities of the present formulation and the formulations proposed in [1] and [3] are highlighted. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||