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Dynamic Problems (dynamic + problem)
Selected AbstractsA new family of generalized-, time integration algorithms without overshoot for structural dynamicsEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 12 2008Yu KaiPing Abstract A new family of generalized-, (G-,) algorithm without overshoot is presented by introducing seven free parameters into the single-step three-stage formulation for solution of structural dynamic problems. It is proved through finite difference analysis that these algorithms are unconditionally stable, second-order accurate and numerical dissipation controllable. The comparison of the new G-, algorithms with the commonly used G-, algorithms shows that the newly developed algorithms have the advantage of eliminating the overshooting characteristics exhibited by the commonly used algorithms while their excellent property of dissipation is preserved. The numerical simulation results obtained using a single-degree-of-freedom system and a two-degree-of-freedom system to represent the character of typical large systems coincide well with the results of theoretical analyses. Copyright © 2008 John Wiley & Sons, Ltd. [source] Numerical modelling of dynamic consolidation on granular soilsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2008S. López-Querol Abstract The application of Pastor,Zienkiewicz constitutive model for sands to dynamic consolidation problems is presented in this paper. This model is implemented in a coupled code formulated in terms of displacements for both solid and fluid phases (u,w formulation), which is firstly compared with u,pw formulation for some simple examples. Its range of validity, previously established for elastic problems and harmonic loading, is explored. Once the suitability of the u,w formulation has been ascertained for this kind of dynamic problems in soils, one- and two-dimensional (plane strain) dynamic consolidation numerical examples are provided, aiming to give some light into the physics of this ground improvement technique. A ,wave of dryness', observed at the soil surface during the impact in field cases, is numerically reproduced and justified. Some hints on the influence of the loading zone size are also given. Copyright © 2007 John Wiley & Sons, Ltd. [source] Nonlinear transient dynamic analysis by explicit finite element with iterative consistent mass matrixINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2009Shen Rong Wu Abstract Various mass matrices in the explicit finite element analyses of nonlinear transient dynamic problems are investigated. The matrices are obtained as a linear combination of lumped and consistent mass matrices. An iterative procedure to calculate the inverse of the consistent and the mixed mass matrices in the framework of explicit finite element method is presented. The convergence of the iterative procedure is proved. The inverse of the consistent and mixed mass matrices is approximated by the iteration and is used to compare the results from the lumped mass matrix. For the impact of a structural component and a vehicle, some difference in the results by using coarse mesh is observed. For the component using fine mesh, no significant difference is found. Copyright © 2008 John Wiley & Sons, Ltd. [source] The radial integration method applied to dynamic problems of anisotropic platesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2007E. L. Albuquerque Abstract In this paper, the radial integration method is applied to transform domain integrals into boundary integrals in a boundary element formulation for anisotropic plate bending problems. The inertial term is approximated with the use of radial basis functions, as in the dual reciprocity boundary element method. The transformation of domain integrals into boundary integrals is based on pure mathematical treatments. Numerical results are presented to verify the validity of this method for static and dynamic problems and a comparison with the dual reciprocity boundary element method is carried out. Although the proposed method is more time-consuming, it presents some advantages over the dual reciprocity boundary element method as accuracy and the absence of particular solutions in the formulation. Copyright © 2006 John Wiley & Sons, Ltd. [source] A new algorithm of time stepping in the non-linear dynamic analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2001Yang Haitian Abstract This paper presents a new scheme of time stepping for solving non-linear dynamic problems. By expanding variables in a discretized time interval, FEM-based recurrent formulae are derived leading to a self-adaptive algorithm for different sizes of time steps. There will be no requirement of iteration for the non-linear solutions. Numerical validation shows satisfactory results. Copyright © 2001 John Wiley & Sons, Ltd. [source] An 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] Stabilized updated Lagrangian corrected SPH for explicit dynamic problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2007Y. Vidal Abstract Smooth particle hydrodynamics with a total Lagrangian formulation are, in general, more robust than finite elements for large distortion problems. Nevertheless, updating the reference configuration may still be necessary in some problems involving extremely large distortions. However, as discussed here, a standard updated formulation suffers the presence of zero-energy modes that are activated and may completely spoil the solution. It is important to note that, unlike an Eulerian formulation, the updated Lagrangian does not present tension instability but only zero-energy modes. Here a stabilization technique is incorporated to the updated formulation to obtain an improved method without any mechanisms and which is capable to solve problems with extremely large distortions. Copyright © 2006 John Wiley & Sons, Ltd. [source] Design, analysis, and synthesis of generalized single step single solve and optimal algorithms for structural dynamicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2004X. Zhou Abstract The primary objectives of the present exposition are to: (i) provide a generalized unified mathematical framework and setting leading to the unique design of computational algorithms for structural dynamic problems encompassing the broad scope of linear multi-step (LMS) methods and within the limitation of the Dahlquist barrier theorem (Reference [3], G. Dahlquist, BIT 1963; 3: 27), and also leading to new designs of numerically dissipative methods with optimal algorithmic attributes that cannot be obtained employing existing frameworks in the literature, (ii) provide a meaningful characterization of various numerical dissipative/non-dissipative time integration algorithms both new and existing in the literature based on the overshoot behavior of algorithms leading to the notion of algorithms by design, (iii) provide design guidelines on selection of algorithms for structural dynamic analysis within the scope of LMS methods. For structural dynamics problems, first the so-called linear multi-step methods (LMS) are proven to be spectrally identical to a newly developed family of generalized single step single solve (GSSSS) algorithms. The design, synthesis and analysis of the unified framework of computational algorithms based on the overshooting behavior, and additional algorithmic properties such as second-order accuracy, and unconditional stability with numerical dissipative features yields three sub-classes of practical computational algorithms: (i) zero-order displacement and velocity overshoot (U0-V0) algorithms; (ii) zero-order displacement and first-order velocity overshoot (U0-V1) algorithms; and (iii) first-order displacement and zero-order velocity overshoot (U1-V0) algorithms (the remainder involving high-orders of overshooting behavior are not considered to be competitive from practical considerations). Within each sub-class of algorithms, further distinction is made between the design leading to optimal numerical dissipative and dispersive algorithms, the continuous acceleration algorithms and the discontinuous acceleration algorithms that are subsets, and correspond to the designed placement of the spurious root at the low-frequency limit or the high-frequency limit, respectively. The conclusion and design guidelines demonstrating that the U0-V1 algorithms are only suitable for given initial velocity problems, the U1-V0 algorithms are only suitable for given initial displacement problems, and the U0-V0 algorithms are ideal for either or both cases of given initial displacement and initial velocity problems are finally drawn. For the first time, the design leading to optimal algorithms in the context of a generalized single step single solve framework and within the limitation of the Dahlquist barrier that maintains second-order accuracy and unconditional stability with/without numerically dissipative features is described for structural dynamics computations; thereby, providing closure to the class of LMS methods. Copyright © 2003 John Wiley & Sons, Ltd. [source] Increasing stable deformation by declining temperature during the processMATERIALWISSENSCHAFT UND WERKSTOFFTECHNIK, Issue 4-5 2008J. Ziegelheim Abstract Recently increasing amount of light metal sheets, especially based on magnesium, is being involved into various structural constructions and functional components. Such a rising trend can be observed, for instance, at automotive, aerospace and electronic industry. On the other hand there exist some processing difficulties, such as forming limits, caused by crystalline structure. To make processing of magnesium materials most reasonable with a maximum economical and material's effect, detailed investigation of the material's mechanical behavior is necessary to realize. Especially, an use of superplasticity is a point of the main interest. By optimum settings of the deformation process (especially temperature and strain rate) the superplastic conditions were determined optimally. Moreover, it was discovered that variable temperature very positively affects the superplasticity of magnesium materials. Actually by changing temperature conditions during the deformation, even higher level of superplastic deformation without rupture can be obtained. This very interesting fact was observed at the elevated temperatures that decrease almost constantly during the deformation process. Thus previously widely used constant temperature treatment opens door to the dynamic problems of searching for the optimal temperature gradient and its variation. [source] The piecewise full decoupling method for dynamic problemsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003Dr.-Ing., Nenad Kranj The piecewise full decoupling method is a new developed numerical procedure of explicit integration based on piecing together local linear solutions. The method is applied for solving piecewise linear dynamic systems under periodic excitations. Close agreement is found between obtained results and published findings of a harmonic balance method and a finite element method in time domain. [source] | ||||||||||