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Summary: An approximate static solution is derived for the elastic settlement and load‐transfer mechanism in axially loaded end‐bearing piles in inhomogeneous soil obeying a power law variation in shear modulus with depth. The proposed generalised formulation can handle different types of soil inhomogeneity by employing pertinent eigenexpansions of the dependent variables over the vertical coordinate, in the form of static soil "modes", analogous to those used in structural dynamics. Contrary to available models for homogeneous soil, the associated Fourier coefficients are coupled, obtained as solutions to a set of simultaneous algebraic equations of equal rank to the number of modes considered. Closed‐form solutions are derived for the (1) pile head stiffness; (2) pile settlement, axial stress, and side friction profiles leading to actual, depth‐dependent Winkler moduli, (3) displacement and stress fields in the soil; and (4) average, depth‐independent Winkler moduli to match pile head settlement. The predictive power of the model is verified via comparisons against finite element analyses. The applicability to inhomogeneous soil of an existing regression formula for the average Winkler modulus is explored. [ABSTRACT FROM AUTHOR]

This study discusses model reduction techniques for second-order index 3 descriptor systems using the balanced truncation methods; in particular, linearised equations of motion with holonomic constraints are considered which arise in mechanics and multibody dynamics. It is shown that the index 3 system can be converted into an equivalent form of index 0 system by projecting it onto the hidden manifold. When model reduction is applied to the projected system, explicit formulation of the projected system is not required. The low-rank alternating direction implicit iteration is also discussed for solving the projected Lyapunov equations of the underlying descriptor system efficiently in an implicit way. The theoretical results are illustrated by numerical experiments. [ABSTRACT FROM AUTHOR]

Elastic bearing of ropeway towers on top of a hotel building A concept of an elastic bearing system by reinforced rubber elements was developed for the insulation of vibrations and structure‐borne noise of two girders, two deflection towers and a motor station of a circular ropeway on top of a newly constructed building. The target was to reduce the vibration immissions as well as the noise which is radiated from transmitted structure‐borne noise. The main difficulties occurred in defining realistic dynamic forces and applicable impedances of the building structure. The design was carried out by the aid of three‐dimensional finite‐element models. The results of measurements while the ropeway was set into operation showed that the constructions work properly and the contractual target criteria were met. [ABSTRACT FROM AUTHOR]

In this paper, a method is presented to determine the vibrational behavior of an electric motor and the associated structure. Therefore, a holistic simulation approach is used, which takes into account the mutual influence of structural mechanics and electrodynamics. For this purpose, a multi body simulation (MBS) is extended so that electromagnetic loads can be considered, which are calculated by using the finite element method (FEM). In electric machines an undisturbed and constant magnetic field is of great importance. Even small variations of the air gap lead to changes in the magnetic field compared to the ideal geometry, which cause a change in the resulting torque and vibration excitation. Especially local and global asymmetric air gap changes due to load‐ and operation‐dependent deformations of the stator and rotor are problematic. Such deformations result on the one hand from the electromagnetically excited structural vibrations and on the other hand from the rotordynamic loads. For these reasons, it is necessary to consider the electro‐ and structural‐dynamic effects together. The developed method is presented on a simple generic motor to show the influence of the coupling. [ABSTRACT FROM AUTHOR]

It is pivotal to predict the multiaxial vibration fatigue life during mechanical structural dynamics design. An algorithm of the finite element method implementation for multiaxial high cycle fatigue life evaluation is proposed, on the basis of elastic evolution model of continuum damage mechanics. By considering structural dynamic characteristics, namely, resonant frequencies and mode shapes, this algorithm includes a modal analysis and harmonic analysis, which makes this different from existing fatigue life prediction methods. A 10% decrease in the resonant frequency is regarded as the failure criterion. A critical damage value was obtained, which indicates mesocrack initiation fulfilment. To validate the effectiveness of the algorithm, auto-phase sine resonance track-and-dwell experiments were conducted on notched cantilever beams made of Ti-6Al-4V alloy. The life predictions are conservative and in good agreements with the experimental results, which are mainly distributed within a scatter band of 2. This investigation could provide technical support for structural dynamics design and the analysis of reusable spacecraft. [ABSTRACT FROM AUTHOR]

The theoretical results relevant to the vibration modes of Timoshenko beams are here used as benchmarks for assessing the correctness of the numerical values provided by several finite element models, based on either the traditional Lagrangian interpolation or on the recently developed isogeometric approach. Comparison of results is performed on both spectrum error (in terms of the detected natural frequencies) and on the l2 relative error (in terms of the computed eigenmodes): this double check allows detecting for each finite element model, and for a discretization based on the same number of degrees-of-freedom, N, the frequency threshold above which some prescribed accuracy level is lost, and results become more and more unreliable. Hence a quantitative way of measuring the finite element performance in modeling a Timoshenko beam is proposed. The use of Fast Fourier Transform is finally employed, for a selected set of vibration modes, to explain the reasons of the accuracy decay, mostly linked to a poor separation of the natural frequencies in the spectrum, which is responsible of some aliasing of modes. [ABSTRACT FROM AUTHOR]

In this paper, a method for vibration analysis of electric engines and associated structure is presented. For this purpose, a multi‐body simulation (MBS) is extended in such a way that electromagnetic loads can be considered using the finite element method (FEM). Subsequently, the determined loads lead to an excitation of the structural vibrations and a sound radiation of the engine, which is analyzed at selected operating points. A test rig will be used to validate the implemented method. Finally, different design variations of the engine are evaluated with respect to their acoustic behavior. The developed method is not limited to the presented application, but it can be applied to any system with electric drives. [ABSTRACT FROM AUTHOR]

This paper presents a superposition method expanded for computing impedance functions (IFs) of inclined-pile groups. Closed-form solutions for obtaining horizontal, vertical, and rocking IFs, estimated by using pile-to-pile interaction factors, are proposed. IFs of solitary inclined piles, crossed IFs, and explicit incorporation of compatibility conditions for pile-head movements are also appropriately taken into consideration. All of these factors should be known in advance and will be computed and shown for the most relevant cases. The accuracy of the proposed closed-form solutions is verified for 2 × 2 and 3 × 3 square inclined-pile groups embedded in an isotropic viscoelastic homogeneous half-space soil medium, with hysteretic damping. The pile-to-pile interaction factors are computed by means of a three-dimensional time-harmonic boundary elements-finite elements coupling formulation. The results indicate that the IFs obtained from the proposed method are in good agreement with those obtained from the coupling formulation. Furthermore, crossed vertical-rocking IFs of solitary piles need to be appropriately considered for obtaining rocking IFs when the number of piles is small. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes a simple numerical method to simulate ductile failure behaviours of tensile plates with interacting through-wall cracks. The method is based on the finite element damage analysis using the stress-modified fracture strain damage model. To validate the proposed method, simulated results are compared with a total of 23 published experimental data of flat tensile plates with interacting through-wall cracks. Despite its simplicity, the proposed method well predicted the experimental maximum loads of tensile plates with interacting cracks, including the loads for crack coalescence. Systematic analyses are also performed to investigate the effect of the element size used in the finite element damage analysis. [ABSTRACT FROM AUTHOR]

Spectral, hierarchical, and h-type finite elements (FEs) are compared in the context of their application to structural dynamics analysis. The Timoshenko beam, which is the 1-D analog of Mindlin-type shell elements, is used for comparison in eigenvalue and transient-response analyses. A detailed formulation of each method is presented to illustrate clearly their fundamental differences. The principal advantages of spectral FEs over low-order h-type elements are (a) far superior accuracy for a fixed number of model degrees of freedom (DOF) and (b) much higher computational efficiency at a fixed accuracy level. The principal advantages over hierarchical p-type elements are (a) a mass matrix that is inherently diagonal as opposed to full, (b) DOF that pertain directly to nodal displacements and rotations, and (c) more efficient tensor-product factorization. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The unsteady interaction between an incompressible fluid and a deformable elastic structure is analyzed. An implicit numerical method is proposed. At each time step, the stresses at the fluid–structure interface are determined as a solution of an optimization problem. The modal decomposition of the structure equations leads to a problem to be solved with a reduced number of unknowns. The analytic gradient of the cost function was derived. Numerical tests validate the analytic derivative and show the behavior of a two-dimensional Navier–Stokes equations with plate-like model interaction. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Massive parallel computers have become more attractive for advanced numerical simulations since standard libraries for communication and synchronization; for example MPI have facilitated program development. The present paper discusses two parallel explicit time integration methods for wave propagation problems; the central difference method and the explicit version of the P1–P1 discontinuous galerkin (DG) method. Based on the MIMD model, where data decomposition is accomplished by element-based grid partitioning, parallel versions of both algorithms have been implemented, using the same paradigm for inter-process communication. Numerical examples are illustrated and the achieved performance of the algorithms is discussed. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Based on energy functional and with the inclusion of high-order incompatible dynamic displacement modes, a formulation for 3-D finite dynamic element method (DEM) is developed and a new 8-node solid element is derived in this paper. Numerical results exhibit that the present method provides the most economical and efficient solution when compared with the usual FEM and DEM. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In a dynamic unbounded medium–structure interaction analysis in the time domain performed with the substructure method the unit-impulse response function on the structure–medium interface of the unbounded medium is determined. The consistent infinitesimal finite element cell method based solely on the finite element formulation has been developed for compressible elasticity. In this paper the procedure is expanded to the incompressible case. The limit of Poisson's ratio =0·5 is performed analytically. This yields a concentrated mass in the formulation representing the instantaneous response over the entire domain not present in compressible elasticity. The only modification appears in the coefficient matrices of the consistent infinitesimal finite element equation which can be solved with the same numerical algorithm as in the compressible case. Excellent accuracy results also in very complicated inhomogeneous situations. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Numerically stable and accurate time integration methods are important in structural dynamics. We propose such a method based on a mixed variational formulation of the underlying semi‐discrete equations of motion. The newly developed scheme relies on a specific combination of the so‐called continuous Galerkin (cG(k)) method and the discontinuous Galerkin (dG(k)) method. We refer to [2] for an introduction of the original cG(k) and dG(k) methods for ODEs (see also [1]). The mixed approach relies on polynomial approximations of degree k on the level of each time finite element. In particular we make use of hierarchical interpolation polynomials. The present approach is closely related to Hellinger‐Reissner type mixed variational formulations for elastodynamics. The mixed method yields implicit time‐stepping schemes with order of accuracy equal to 2k for the displacements and velocities. In addition to that, the method is capable of conserving the energy in the case of conservative mechanical systems. Numerical examples are presented which highlight the numerical properties of the newly proposed mixed approach. [ABSTRACT FROM AUTHOR]

Disc brakes convert kinetic energy into thermal energy in order to slow down vehicles. During the braking process enormous heat flows and temperature gradients occur in the system. Because heating leads to a change in shape for most materials, it is important to take the temperature and its influence into account during the design process. The interaction between the structure and the heat in disc brakes can be described with methods from thermoelasticity. To simulate thermoelastic behaviour the Finite Element Method is commonly used. The thermal and mechanical domain are taken into account by coupling the equation of motion and the heat equation. However, in transient analysis often the problem occurs of different time scales of the structural and thermal dynamics for many technically relevant materials, like steel. For metallic materials the time constant of structural dynamics is much smaller than those of thermal dynamics. This complicates an efficient transient simulation. In the present work the implementation of a Finite Element Method in thermoelasticity and associated investigations are shown. The method is applied to various parts and load cases. Also different approaches to deal with the different time scales will be shown. Heuristic methods like mass‐scaling as well as more mathematically oriented approaches like model order reduction are presented. [ABSTRACT FROM AUTHOR]

Abstract: We apply a multipreconditioned domain decomposition method based on Finite Element Tearing and Interconnecting to linear structural dynamics with highly heterogeneous material properties. A recently published method to build and select the multiple directions is presented and applied. We hint at possible problems when localized phenomena are considered and present a new simple measure that extends the selection process in existing algorithms. We show numerical results and conclude how to effectively prevent a possible degeneration of the minimization space basis. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Computational costs for detailed Finite Element approximations can be reduced by using reduced-order models instead. In this contribution, four subspace-based reduced-order modeling methods are compared. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In structural dynamics the initial boundary-value problem has to be solved in the space and time domain. The spatial discretization is done using finite elements yielding systems of differential equations of second-order. Incorporating inelastic material properties, thermo-mechanical coupling and particular Dirichlet boundary conditions essentially changes the underlying mathematical problem. The main goal is to provide higher-order time integration schemes using diagonally-implicit Runge-Kutta methods (DIRK) and the Generalized α-method consistently applied to the semi-discretized ODE-system comprising the semi-discretized equations of motion, the unsteady semi-discrete heat equation and constitutive equations of evolutionary-type. Furthermore, we want to show the applicability of time-adaptivity by embedded schemes so that step-sizes are chosen automatically. The inelastic constitutive equations are given by a thermo-viscoplasticity model of Perzyna/Chaboche-type with non-linear kinematic hardening. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In the present paper we consider structure-preserving integration methods in the context of mixed finite elements. The used low-order mixed finite elements typically exhibit improved coarse mesh accuracy. On the other hand energy-momentum (EM) consistent time-stepping schemes have been developed in the realm of nonlinear structural dynamics to enhance the numerical stability properties. EM schemes typically exhibit superior robustness and thus offer the possibility to use large time steps while still producing physically meaningful results. Accordingly, combining mixed finite element discretizations in space with EM consistent discretizations in time shows great promise for the design of numerical methods with superior coarse mesh accuracy in space and time. Starting with a general Hu-Washizu-type variational formulation we develop a second-order accurate structure-preserving integration scheme. The present approach is applicable to a large number of mixed finite element formulations. As sample application we deal with a specific mixed shell element. Numerical examples dealing with large deformations will show the improved coarse mesh accuracy in space and time of the advocated approach. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Computational resources can be used more efficiently by introducing reduced-order models, instead of solving large systems of equations of the original model. In this contribution, the Krylov subspace method, a reduced-order modeling method, is studied and compared to the modal decomposition for a rubber wheel model. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Explicit time integration has proven to be highly suitable for the simulation of very fast processes and highly nonlinear applications. As is well known the time integration algorithm is only stable if the Courant-Friedrichs-Lewy criterion is fulfilled leading usually to very small time step sizes. As a result the efficiency of the time integration algorithm is dictated by the computational time of element operations. In structural mechanics low order finite elements are attractive due to their efficiency but introduce artificial stiffness effects. To resolve the so-called locking effects a transient description - suitable for the solution in the context of explicit time integration - of the method of enhanced assumed strains (EAS) is formulated utilizing a generalization of the method of incompatible modes (IM). The element routines are computationally realised applying symbolic programming. The functionality and achieved efficiency are demonstrated on a numeric example. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]