Analysis of polyhedral domed structures composed of flat plates of sandwich material

Not availabl

On wave boundary elements for radiation and scattering problems with piecewise constant impedance

Discrete methods of numerical analysis have been used successfully for decades for the solution of problems involving wave diffraction, etc. However, these methods, including the finite element and boundary element methods, can require a prohibitively large number of elements as the wavelength becomes progressively shorter. In this paper, a new type of interpolation for the wave field is described in which the usual conventional shape functions are modified by the inclusion of a set of plane waves propagating in multiple directions. Including such a plane wave basis in a boundary element formulation is found in this paper to be highly successful. Results are shown for a variety of scattering/radiating problems from convex and nonconvex obstacles on which are prescribed piecewise constant Robin conditions. Notable results include a conclusion that, using this new formulation, only approximately three degrees of freedom per wavelength are required

Ground Waves Generated by Pile Driving, and Structural Interaction

Pre-formed steel or concrete pile elements are installed by high energy impact or vibro-driver, which causes outgoing ground waves. In severe cases, adjacent buildings are at risk of damage. Assessment of risk is conventionally by reference to threshold limits of vibration. The global approach considers neither the interactive effects between ground and structure, nor frequency and duration. Here, firstly, the dynamics of a pile head impact and of the transmission of a portion of the energy into the ground were modelled by a combination of finite elements (FE), springs and dashpots. The boundary disturbances were then applied to a second model of the soil as an elastic half space. This outer model was constructed of axisymmetric finite and infinite elements for calibration against on-site measurements. The infinite elements (IE) represented a wider zone, and avoided spurious wave reflections at boundaries. Next, the verified ground disturbances adjacent to the pile were used as input to a three-dimensional FE/IE wedge-shaped model of a ‘slice’ of the axisymmetric system. Various structural forms, of steel frame structures and of brick walls, were added, giving a dynamic soil-structure analysis. Results show the responses of flexible and stiff structures to outgoing waves caused by impact pile driving and vibro-driving

Tomographic imaging and scanning thermal microscopy: thermal impedance tomography

The application of tomographic imaging techniques developed for medical applications to the data provided by the scanning thermal microscope will give access to true three-dimensional information on the thermal properties of materials on a mm length scale. In principle, the technique involves calculating and inverting a sensitivity matrix for a uniform isotropic material, collecting ordered data at several modulation frequencies, and multiplying the inverse of the matrix with the data vector. In practice, inversion of the matrix in impractical, and a novel iterative technique is used. Examples from both simulated and real data are given

Formation of a primitive ectoderm like cell population, EPL cells, from ES cells in response to biologically derived factors

The primitive ectoderm of the mouse embryo arises from the inner cell mass between 4.75 and 5.25 days post coitum, around the time of implantation. Positioned at a pivotal time in development, just prior to formation of the three germ layers of the embryo proper, the primitive ectoderm responds directly to the signals generated during gastrulation. We have identified a conditioned medium, MEDII, which caused the homogeneous conversion of ES cells to a morphologically distinct cell population, termed early primitive ectoderm-like (EPL) cells. EPL cells expressed the pluripotent cell markers Oct4, SSEA1 and alkaline phosphatase. However, the formation of EPL cells was accompanied by alterations in Fgf5, Gbx2 and Rex1 expression, a loss in chimaera forming ability, changes in factor responsiveness and modified differentiation capabilities, all consistent with the identification of EPL cells as equivalent to the primitive ectoderm population of the 5.5 to 6.0 days post coitum embryo. EPL cell formation could be reversed in the presence of LIF and withdrawal of MEDII, which suggested that EPL cell formation was not a terminal differentiation event but reflected the ability of pluripotent cells to adopt distinct cell states in response to specific factors. Partial purification of MEDII revealed the presence of two separable biological activities, both of which were required for the induction and maintenance of EPL cells. We show here the first demonstration of uniform differentiation of ES cells in response to biological factors. The formation of primitive ectoderm, both in vivo and in vitro, appears to be an obligatory step in the differentiation of the inner cell mass or ES cells into cell lineages of the embryonic germ layers. EPL cells potentially represent a model for the development of lineage specific differentiation protocols and analysis of gastrulation at a molecular level. An understanding of the active components of MEDII may provide a route for the identification of factors which induce primitive ectoderm formation in vivo.Joy Rathjen, Julie-Anne Lake, Michael D. Bettess, Jenny M. Washington, Gavin Chapman and Peter D. Rathje

A high-wavenumber boundary-element method for an acoustic scattering problem

In this paper we show stability and convergence for a novel Galerkin boundary element method approach to the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data. This problem models, for example, outdoor sound propagation over inhomogeneous flat terrain. To achieve a good approximation with a relatively low number of degrees of freedom we employ a graded mesh with smaller elements adjacent to discontinuities in impedance, and a special set of basis functions for the Galerkin method so that, on each element, the approximation space consists of polynomials (of degree $\nu$) multiplied by traces of plane waves on the boundary. In the case where the impedance is constant outside an interval $[a,b]$, which only requires the discretization of $[a,b]$, we show theoretically and experimentally that the $L_2$ error in computing the acoustic field on $[a,b]$ is ${\cal O}(\log^{\nu+3/2}|k(b-a)| M^{-(\nu+1)})$, where $M$ is the number of degrees of freedom and $k$ is the wavenumber. This indicates that the proposed method is especially commendable for large intervals or a high wavenumber. In a final section we sketch how the same methodology extends to more general scattering problems

Self Designing Structures: a new evolutionary rule for thickness distribution in 2D problems

International audienceThis paper deals with an evolutionary rule for material distribution in topology optimization problems. This rule is determined in order to satisfy the design constraints that can appear in an industrial design problem. Some other topology optimization techniques are presented before describing our scheme. The classical MBB problem is used to illustrate the capabilities of our approach. The influences of a design parameter and the mesh refinement are discussed

Parallel computation of 3-D soil-structure interaction in time domain with a coupled FEM/SBFEM approach

The final publication is available at Springer via http://dx.doi.org/10.1007/s10915-011-9551-xThis paper introduces a parallel algorithm for the scaled boundary finite element method (SBFEM). The application code is designed to run on clusters of computers, and it enables the analysis of large-scale soil-structure-interaction problems, where an unbounded domain has to fulfill the radiation condition for wave propagation to infinity. The main focus of the paper is on the mathematical description and numerical implementation of the SBFEM. In particular, we describe in detail the algorithm to compute the acceleration unit impulse response matrices used in the SBFEM as well as the solvers for the Riccati and Lyapunov equations. Finally, two test cases validate the new code, illustrating the numerical accuracy of the results and the parallel performances. © Springer Science+Business Media, LLC 2011.Jose E. Roman and Enrique S. Quintana-Orti were partially supported by the Spanish Ministerio de Ciencia e Innovacion under grants TIN2009-07519, and TIN2008-06570-C04-01, respectively.Schauer, M.; Román Moltó, JE.; Quintana Orti, ES.; Langer, S. (2012). Parallel computation of 3-D soil-structure interaction in time domain with a coupled FEM/SBFEM approach. Journal of Scientific Computing. 52(2):446-467. doi:10.1007/s10915-011-9551-xS446467522Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., Croz, J.D., Greenbaum, A., Hammarling, S., McKenney, A., Sorensen, D.: LAPACK User’s Guide. Society for Industrial and Applied Mathematics, Philadelphia (1992)Antes, H., Spyrakos, C.: Soil-structure interaction. In: Beskos, D., Anagnotopoulos, S. (eds.) Computer Analysis and Design of Earthquake Resistant Structures, p. 271. Computational Mechanics Publications, Southampton (1997)Appelö, D., Colonius, T.: A high-order super-grid-scale absorbing layer and its application to linear hyperbolic systems. J. Comput. Phys. 228(11), 4200–4217 (2009)Astley, R.J.: Infinite elements for wave problems: a review of current formulations and a assessment of accuracy. Int. J. Numer. Methods Eng. 49(7), 951–976 (2000)Balay, S., Buschelman, K., Eijkhout, V., Gropp, W.D., Kaushik, D., Knepley, M., McInnes, L.C., Smith, B.F., Zhang, H.: PETSc users manual. Tech. Rep. ANL-95/11 - Revision 3.1, Argonne National Laboratory (2010)Benner, P.: Contributions to the numerical solution of algebraic Riccati equations and related eigenvalue problems. Dissertation, Fak. f. Mathematik, TU Chemnitz–Zwickau, Chemnitz, FRG (1997)Benner, P.: Numerical solution of special algebraic Riccati equations via an exact line search method. In: Proc. European Control Conf. ECC 97, Paper 786, BELWARE Information Technology, Waterloo (B) (1997)Benner, P., Quintana-Ortí, E.: Solving stable generalized Lyapunov equations with the matrix sign function. Numer. Algorithms 20(1), 75–100 (1999)Benner, P., Byers, R., Quintana-Ortí, E., Quintana-Ortí, G.: Solving algebraic Riccati equations on parallel computers using Newton’s method with exact line search. Parallel Comput. 26(10), 1345–1368 (2000)Benner, P., Quintana-Ortí, E.S., Quintana-Ortí, G.: Solving linear-quadratic optimal control problems on parallel computers. Optim. Methods Softw. 23(6), 879–909 (2008)Bettess, P.: Infinite Elements. Penshaw Press, Sunderland (1992)Blackford, L.S., Choi, J., Cleary, A., D’Azevedo, E., Demmel, J., Dhillon, I., Dongarra, J., Hammarling, S., Henry, G., Petitet, A., Stanley, K., Walker, D., Whaley, R.C.: ScaLAPACK Users’ Guide. Society for Industrial and Applied Mathematics, Philadelphia (1997)Borsutzky, R.: Braunschweiger Schriften zur Mechanik - Seismic Risk Analysis of Buried Lifelines, vol. 63. Mechanik-Zentrum Technische Universität. Braunschweig (2008)Dongarra, J.J., Whaley, R.C.: LAPACK working note 94: A user’s guide to the BLACS v1.1. Tech. Rep. UT-CS-95-281, Department of Computer Science, University of Tennessee (1995)Engquist, B., Majda, A.: Absorbing boundary conditions for the numerical simulation of waves. Math. Comput. 31(139), 629–651 (1977)Granat, R., Kågström, B.: Algorithm 904: The SCASY library – parallel solvers for Sylvester-type matrix equations with applications in condition estimation, part II. ACM Trans. Math. Softw. 37(3), 33:1–33:4 (2010)Guerrero, D., Hernández, V., Román, J.E.: Parallel SLICOT model reduction routines: The Cholesky factor of Grammians. In: Proceedings of the 15th Triennal IFAC World Congress, Barcelona, Spain (2002)Harr, M.E.: Foundations of Theoretical Soil Mechanics. McGraw-Hill, New York (1966)Hilbert, H., Hughes, T., Taylor, R.: Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Eng. Struct. Dyn. 5, 283 (1977)Kleinman, D.: On an iterative technique for Riccati equation computations. IEEE Trans. Autom. Control AC-13, 114–115 (1968)Lehmann, L.: Wave Propagation in Infinite Domains. Springer, Berlin (2006)Lehmann, L., Langer, S., Clasen, D.: Scaled boundary finite element method for acoustics. J. Comput. Acoust. 14(4), 489–506 (2006)Liao, Z.P., Wong, H.L.: A transmitting boundary for the numerical simulation of elastic wave propagation. Soil Dyn. Earthq. Eng. 3(4), 174–183 (1984)Lysmer, J., Kuhlmeyer, R.L.: Finite dynamic model for infinite media. J. Eng. Mech. 95, 859–875 (1969)Meskouris, K., Hinzen, K.G., Butenweg, C., Mistler, M.: Bauwerke und Erdbeben - Grundlagen - Anwendung - Beispiele. Vieweg Teubner, Wiesbaden (2007)MPI Forum: The message passing interface (MPI) standard (1994). http://www.mcs.anl.gov/mpiNewmark, N.: A method of computation for structural dynamics. J. Eng. Mech. Div. 85, 67 (1959)Petersen, C.: Dynamik der Baukonstruktionen. Vieweg/Sohn Verlagsgesellschaft, Braunschweig (2000)Roberts, J.: Linear model reduction and solution of the algebraic Riccati equation by use of the sign function. Int. J. Control 32, 677–687 (1980)Schauer, M., Lehmann, L.: Large scale simulation with scaled boundary finite element method. Proc. Appl. Math. Mech. 9, 103–106 (2009)Wolf, J.: The Scaled Boundary Finite Element Method. Wiley, Chichester (2003)Wolf, J., Song, C.: Finite-Element Modelling of Unbounded Media. Wiley, Chichester (1996

Prediction of 3D grinding temperature field based on meshless method considering infinite element

© 2018, Springer-Verlag London Ltd., part of Springer Nature. A three-dimensional numerical model to calculate the grinding temperature field distribution is presented. The finite block method, which is developed from meshless method, is used to deal with the stationary and the transient heat conduction problems in this paper. The influences of workpiece feed velocity, cooling coefficient, and the depth of cut on temperature distribution are considered. The model with temperature-dependent thermal conductivity and specific heat is presented. The Lagrange partial differential matrix from the heat transfer governing equation is obtained by using Lagrange series and mapping technique. The grinding wheel-workpiece contact area is assumed as a moving distributed square heat source. The Laplace transformation method and Durbin’s inverse technique are employed in the transient heat conduction analysis. The results of the developed model are compared with others’ finite element method solutions and analytical solutions where a good agreement is demonstrated. And the finite block method was proved a better convergence and accuracy than finite element method by comparing the ABAQUS results. In addition, the three-dimensional infinite element is introduced to perform the thermal analysis, and there is a great of advantages in the simulation of large boundary problems.The work was funded by China Scholarship Council, the Fundamental Research Funds for the Central Universities (N160306006), National Natural Science Foundation of China (51275084), and Science and technology project of Shenyang (18006001)