Structural Dynamics Problems Research Articles

A finite element model for coupled 3D transient electromagnetic and structural dynamics problems

This paper develops a framework for coupling transient electromagnetic (EM) and dynamic mechanical (ME) fields to predict the evolution of electrical and magnetic fields and their fluxes in a vibra...

Elastodynamics Model Updating for the Monitoring of Reinforced Concrete Beam: Methodology and Numerical Implementation

Reinforced concrete beams are widely employed in civil engineering structures. To reduce the maintenance financial cost, structure damages have to be detected early. To this end, one needs robust monitoring techniques. The paper deals with the identification of mechanical parameters, useful for Structural Health Monitoring, in a 2D beam using inverse modeling technique. The optimal control theory is employed. As an example, we aim to identify a reduction of the steel bar cross-section and a decrease of the concrete Young modulus in damaged areas. In our strategy, the beam is instrumented with strain sensors, and a known dynamic load is applied. In the inverse technique, two space discretizations are considered: a fine dicretization (h) to solve the structural dynamic problem and a coarse discretization (H) for the beam parameter identification. To get the beam parameters, we minimize a classical data misfit functional using a gradient-like algorithm. A low-cost computation of the functional gradient is performed using the adjoint equation. The inverse problem is solved in a general way using engineer numerical tools: Python scripts and the free finite element software Code_Aster. First results show that a local reduction of the steel bar cross-section and a local decrease of concrete Young modulus can be detected using this inverse technique.

Computationally efficient multi-time-step method for partitioned time integration of highly nonlinear structural dynamics

An efficient and accurate method for solving large-scale problems in non-linear structural dynamics is presented. The method uses dual-Schur domain decomposition to divide a large finite element mesh into a number of smaller subdomains, which are solved independently using a suitable mesh-size and time-step to capture the local spatial and temporal scales of the problem. Continuity of the solution between subdomains is enforced by Lagrange multipliers. It is shown that the proposed method is stable, accurate and computationally more efficient than using a uniform time-step for the entire mesh. Numerical examples are presented to illustrate and corroborate these properties.

Wet damping estimation of the scaled segmented hull model using the random decrement technique

Damping is one of the most uncertain factors in structural dynamic problems, and plays a very important role in resonance phenomena such as springing. This paper presents the wet damping estimation of a segmented hull model using a random decrement technique together with continuous wavelet transform. The 16 sea states were grouped together based on the speed of the ship to determine the possible influence of the ship speed on the damping ratio. The measured time histories of the vertical bending moment for each tested sea state were processed using the random decrement technique to derive the free decay signal, from which the damping ratios were estimated. In addition, the autocorrelation functions of the filtered signal were calculated and a comparison was made with the free decay signal obtained from the random decrement technique. The wet damping ratios for each sea state group, as well as precise wet natural frequencies, were estimated using a continuous wavelet transform. The wet natural frequencies derived from the measured signal did not show any significant discrepancy compared to those obtained using the wet hammering test, whereas a significant discrepancy was observed with the damping ratio. The discrepancy of the damping ratio between in calm and moving water might be due to the viscous effects caused by the dramatically different flow patterns and relative velocity between the vibrating structure and surrounding fluid particles.

동적 문제에 효율적인 적응적 유한요소망

The finite element method has become the most widely used method of structural analysis and recently, the method has often been applied to complex dynamic and nonlinear structural analyses problems. Even for these complex problems, where the responses are hard to predict, finite element analyses yield reliable results if appropriate element types and meshes are used. However, the dynamic and nonlinear behaviors of a structure often include large deformations in various portions of the structure and if the same mesh is used throughout the analysis, some elements may deform to shapes beyond the reliable limits; thus dynamically adapting finite element meshes are needed in order for the finite element analyses to be accurate. In addition, to satisfy the users requirement of quick real run time of finite element programs, the algorithms must be computationally efficient. This paper presents an adaptive finite element mesh generation scheme for dynamic analyses of structures that may adapt at each time step. Representative strain values are used for error estimates and combinations of the h-method(node movement) and the r-method(element division) are used for mesh refinements. A coefficient that depends on the shape of an element is used to limit overly distorted elements. A simple frame example shows the accuracy and computational efficiency of the scheme. The aim of the study is to outline the adaptive scheme and to demonstrate the potential use in general finite element analyses of dynamic and nonlinear structural problems commonly encountered.

Closure to “Applications of asymptotic sampling on high dimensional structural dynamic Problems” by M.T. Sichani, S.R.K. Nielsen and C. Bucher

Closure to “Applications of asymptotic sampling on high dimensional structural dynamic Problems” by M.T. Sichani, S.R.K. Nielsen and C. Bucher

Non-probabilistic convex model process: A new method of time-variant uncertainty analysis and its application to structural dynamic reliability problems

In this paper, we propose a method for time-variant uncertainty analysis, namely, the “non-probabilistic convex model process”, which provides an effective mathematical tool for the analysis of structural dynamic uncertainty when lacking relevant information. In the convex model process, we express the variables at any time with intervals and establish the corresponding auto-covariance function and correlation coefficient function to depict the correlation between variables at different times. We also define several important characteristic parameters for the uni- and bi-dimensional convex model processes, including the mid-value function, variance function, auto-covariance function, and cross-covariance function; we provide the definition for the stationary convex model process and its ergodicity. Then, by combining the convex model process with the first-passage failure mechanism, we propose a non-probabilistic analysis model of structural dynamic reliability and formulate the solving algorithm based on Monte Carlo simulation. Finally, through the analysis of numerical examples, we verify the effectiveness of the convex model process and the model of dynamic reliability analysis proposed in this paper.

Discussion on: Applications of asymptotic sampling on high dimensional structural dynamic problems: M.T. Sichani, S.R.K. Nielsen and C. Bucher, Structural Safety, 33 (2011) 305–316

Article history: Available online 19 October 2013 2013 Elsevier Ltd. All rights reserved. C. Bucher originally proposed the asymptotic sampling (AS) for high dimensional reliability analysis with lower failure probability [1]. Further, M.T. Sichani, S.R.K. Nielsen and C. Bucher developed the AS for the evaluation of high dimensional structural dynamic problems [2]. In their method, the lower failure probability is extrapolated by several high failure probabilities on the asymptotic behavior of the failure probability in n-dimensional independent and identically distributed (i.i.d) Gaussian space with respect to the standard deviation of the variables. The detailed steps of their methods can be summarized as follows: Step 1. Transform the random variables X of the original problem into the i.i.d Gaussian U space, i.e. N, using Rosenblatt transformation or Nataf transformation T: X ? U. Step 2. Choose the parameters fi 2 [0, 1] (i = 1, 2, . . . ,m), and increase the standard deviation of N but keep the mean of N invariant, and then obtain the scaled random variables Nfi . If N NðlN;r2Þ, then Nfi N lN;rN=f 2 i . Step 3. Perform the standard Monte Carlo simulation with Nfi and calculate the scaled failure probability Pf(fi). Step 4. Evaluate the scaled reliability index as b(fi) = U (1 Pf(fi)). Step 5. Obtain all the b(fi) (i = 1, 2, . . . ,m), for different fi to construct a set of (fi, b(fi)) which will be regarded as ‘‘support points’’. Step 6. Estimate coefficients A and B of Eq. (1) using the set of (fi, b(fi)) (i = 1, . . . ,m) by regression analysis. bðfiÞ 1⁄4 Af i þ B fi ð1Þ Step 7. Estimate the un-scaled reliability index b(1) = A + B and the lower failure probability Pf(1) = 1 U(b(1)). As revealed by Steps 1–7, we can find that the main computational cost of the AS lies in the sum of the time for all the b(fi) (i = 1, 2, . . . ,m) by the standard Monte Carlo simulation. Admittedly, the sum of time for b(fi) is generally less than that of the direct evaluation of b(1) and the AS consequentially reduces the computational cost. In addition, this method behaves well when it comes to problems with high nonlinearity and lower failure probability. However, after conducting a detailed investigation into the AS method, we find that there are still three issues necessary to be discussed. The first is that the computational cost in AS may be still prohibitive due to the fact that m independent evaluations of b(fi) are required to obtain the ‘‘support points’’. The second is that sometimes the individual regression analysis using Eq. (1) leads to remarkable discrepancies compared with the accurate result. The third is that the AS is not able to give the confidence interval of the result. In this paper, we discuss these issues for further improving the accuracy and efficiency of the AS method. 1. Discussion to the first issue It is assumed that the performance function is y = G(x). For Pf(fi) (i = 1, 2, . . . ,m), we first construct the same importance sampling probability density function (IS PDF) f (x), then Pf(fi) (i = 1, 2, . . . ,m) can be estimated by the same importance sampling (IS) method through only one set of input–output samples (xk,G(xk)) (k = 1, . . . ,N), where N is the number of samples. Pf 1⁄4 Z F f ðxÞdx 1⁄4 Z IFðxÞ f ðxÞ f ðxÞ f ðxÞdx 1⁄4 E IFðxÞxðxÞ 1⁄2 ð2Þ

Coupling of non‐conforming meshes in a component mode synthesis method

SUMMARYA common mesh refinement‐based coupling technique is embedded into a component mode synthesis method, Craig–Bampton. More specifically, a common mesh is generated between the non‐conforming interfaces of the coupled structures, and the compatibility constraints are enforced on that mesh via L2‐minimization. This new integrated method is suitable for structural dynamic analysis problems where the substructures may have non‐conforming curvilinear and/or surface interface meshes. That is, coupled substructures may have different element types such as shell, solid, and/or beam elements. The proposed method is implemented into a commercial finite element software, B2000++, and its demonstration is carried out using an academic and industry oriented test problems. Copyright © 2013 John Wiley & Sons, Ltd.

Numerical Simulation on Flight Dynamic Characteristics of Elastic Wing Based on Gust Response

In this paper, the numerical method was developed to flight dynamics characteristics of elastic wing under the action of the discrete gust. In this numerical method, the aerodynamic forces of the elastic wing were calculated by solving the unsteady Navier Stokes equations, and incorporating the grid velocity method to simulating the gust response of the typical NACA0006 airfoil to the step changes in the angle of attack of aircraft . it is shown in results that the calculated lift responses of the airfoil agree well with both the exact theoretical value and calculated value in reference. the elastic effect was considered with RayleighRitz method, so that the fluid dynamic,structural dynamic and flight dynamic problems can be coupled to solve. and AGARD445.6 elastic wing for the numerical simulation of the flight characteristics.

Power flow response based dynamic topology optimization of bi-material plate Structures

Work on dynamic topology optimization of engineering structures for vibration suppression has mainly addressed the maximization of eigenfrequencies and gaps between consecutive eigenfrequencies of free vibration, minimization of the dynamic compliance subject to forced vibration, and minimization of the structural frequency response. A dynamic topology optimization method of bi-material plate structures is presented based on power flow analysis. Topology optimization problems formulated directly with the design objective of minimizing the power flow response are dealt with. In comparison to the displacement or velocity response, the power flow response takes not only the amplitude of force and velocity into account, but also the phase relationship of the two vector quantities. The complex expression of power flow response is derived based on time-harmonic external mechanical loading and Rayleigh damping. The mathematical formulation of topology optimization is established based on power flow response and bi-material solid isotropic material with penalization(SIMP) model. Computational optimization procedure is developed by using adjoint design sensitivity analysis and the method of moving asymptotes(MMA). Several numerical examples are presented for bi-material plate structures with different loading frequencies, which verify the feasibility and effectiveness of this method. Additionally, optimum results between topological design of minimum power flow response and minimum dynamic compliance are compared, showing that the present method has strong adaptability for structural dynamic topology optimization problems. The proposed research provides a more accurate and effective approach for dynamic topology optimization of vibrating structures.

응력 구속조건을 고려한 동하중의 등가정하중으로의 변환

Due to the difficulty in considering dynamic load in the view point of a computer resource and computing time, it is common that external load is assumed as ideal static loads. However, structural analysis under static load cannot guarantee the safety of design of the structures under dynamic loadings. Recently, the systematic method to construct equivalent static load from the given dynamic load has been proposed. Previous study has calculated equivalent static load through the optimization procedure under displacement constraints. However, previously reported works to distribute equivalent static load were based on ad-hoc methods. Improper selection of equivalent static loading positions may results in unreliable prediction of structural design. The present study proposes the selection method of the proper locations of equivalent static loads to dynamically applied loads when we consider transient dynamic structural problems. Moreover, it is appropriate to take into account the stress constraint as well as displacement constraint condition for the safety design. But the previously reported studies of equivalent static load design methods considered only displacement constraint conditions but not stress constraint conditions. In the present study we consider not only displacement constraint but also stress constraint conditions. Through a few numerical examples, the efficiency and reliability of proposed scheme is verified by comparison of the equivalent stress between equivalent static loading and dynamic loading.

Performance of an implicit time integration scheme in the analysis of wave propagations

In earlier work an effective implicit time integration scheme was proposed for the finite element solution of nonlinear dynamic problems [1,2]. The method, referred to as the Bathe method, was shown to possess unusual stability and accuracy characteristics for the solution of problems in linear and nonlinear structural dynamics [1–3]. In this paper we study the dispersion properties of the method, in comparison to those of the widely used Newmark trapezoidal rule, and show that the desired characteristics of the Bathe method for structural dynamics are also seen, and are very important, in the solution of wave propagation problems. A dispersion analysis is given and problems are solved to illustrate the capabilities of the scheme for the solution of wave propagation problems.

BEM-FEM coupling for acoustic effects on aeroelastic stability of structures

A series of work has been carried out to develop the foundation for the computational scheme for the calculation of the influence of the acoustic disturbance to the aeroelastic stability of the structure. The generic approach consists of three parts. The first is the formulation of the acoustic wave propagation governed by the Helmholtz equation by using boundary element approach, which then allows the calculation of the acoustic pressure on the acoustic-structure boundaries. The structural dynamic problem is formulated using finite element approach. The third part involves the calculation of the unsteady aerodynamics loading on the structure using generic unsteady aerodynamics computational method. Analogous to the treatment of dynamic aeroelastic stability problem of structure, the effect of acoustic pressure disturbance to the aeroelastic structure is considered to consist of structural motion independent incident acoustic pressure and structural motion dependent acoustic pressure, referred to as the acoustic aerodynamic analogy. Results are presented and compared to those obtained in earlier work.

Nonlinear Structural Dynamics Analysis Using Weighted Residual Integration

A new time integration method is proposed for solving a differential equation of motion of structural dynamics problems with nonlinear stiffness. In this method, it is assumed that order of variation of acceleration is quadratic in each time step and, therefore, variation of displacement in each time step is a fourth-order polynomial that has five coefficients. Other than implementing initial conditions and satisfying equation of motions at both ends, weighted residual integral is also used in order to evaluate the unknown coefficients. By increasing order of acceleration, more terms of Taylor series are used, which were expected to have better responses than the other classical methods. The proposed method is non-dissipative and its numerical dispersion showed to be clearly less than the other methods. By studying stability of the method, it reveals that critical time step duration for the proposed method can be larger than the critical time step duration obtained from other classical methods; also, computational time for analysis with critical time step duration for the proposed method becomes less in comparison with linear acceleration and central difference methods. The order of accuracy of the proposed method is four, which showed to be very accurate in almost all practical problems.

Explicit Dynamic Finite Element Method for Failure with Smooth Fracture Energy Dissipations

A numerical method for dynamic failure analysis through the phantom node method is further developed. A distinct feature of this method is the use of the phantom nodes with a newly developed correction force scheme. Through this improved approach, fracture energy can be smoothly dissipated during dynamic failure processes without emanating noisy artifact stress waves. This method is implemented to the standard 4-node quadrilateral finite element; a single quadrature rule is employed with an hourglass control scheme in order to decrease computational cost and circumvent difficulties associated with the subdomain integration schemes for cracked elements. The effectiveness and robustness of this method are demonstrated with several numerical examples. In these examples, we showed the effectiveness of the described correction force scheme along with the applicability of this method to an interesting class of structural dynamic failure problems.

Finite-element-wise domain decomposition iterative solvers with polynomial preconditioning

A highly scalable finite-element-wise domain decomposition (EDD) iterative solver (with particular emphasis on the flexible GMRES method) based on polynomial preconditioning is discussed in this paper. Compared to alternative methods, finite-element-wise domain decomposition solvers with polynomial preconditioning circumvent the assembly of the matrix, reordering of the degree-of-freedom, redundant computations associated with the interface elements, numerical problems associated with the local preconditioner, and costly global preconditioner construction. A dramatic reduction in parallel overhead is achieved, both in terms of computation and communication results, in a highly scalable solver. This work is implemented using MPI C++and applied to solve static and dynamic structural mechanics problems. The corresponding numerical performance, with emphasis on iterative convergence and parallel scalability, of the proposed approach over the SGI Origin machine is critically assessed.

Multiscale methods for levitron problems: Theory and applications

A multiscale model based on magneto-static traps of neutral atoms or ion traps is described. The idea is to levitate a magnetic spinning top in the air, repelled by a base magnet. Real-life applications are related to magnetostatic trapping fields, e.g., [1], which allows trapping neutral atoms. In engineering, such effects are used in spectroscopy and atomic clocks, e.g., [2].Such problems are related to nonlinear problems in structural dynamics. The dynamics of such rigid bodies are modeled as a mechanical system with kinetic and potential parts, and can be described by a Hamiltonian, see [3–5].For such a problem, one must deal with different temporal and spatial scales, and so a novel splitting method for solving the levitron problem is proposed, see [6].In the present paper, we focus on explicit and extrapolated time-integrator methods, which are related to the Verlet algorithms. Due to the fact that we can decouple this multiscale problem into a kinetic part T and a potential part U, explicit methods are very appropriate. We try to limit the number of evaluations which are necessary (for a given accuracy) to obtain stable trajectories, and try to avoid the iterative cycles which are involved in implicit schemes, see [7].The kinetic and potential parts can be seen as generators of flows, see [5].The main problem is that of accurately formulating the Hamiltonian equation and this paper proposes a novel higher order splitting scheme to obtain stable states near the relative equilibrium. To improve the splitting scheme, a novel method, called MPE (multiproduct expansion method), is applied (see [8]), which includes higher order extrapolation schemes.The stability near this relative equilibrium is discussed with numerical studies using novel improved time-integrators. The best results are obtained with extrapolated Verlet schemes rather than higher order explicit Runge–Kutta schemes. Experiments are carried out with a magnetic top in an axisymmetric magnetic field (i.e., the levitron) and future applications to quantum computation will be discussed.

Application of Improved Response Surface Method Based on Kriging Model to Structural Reliability Analysis

The paper aims to do the reliability analysis by the Kriging model. Its excellent approximating capability is taken into consideration, which is superior to traditional response surface method. An improved response surface method has been proposed based on the Kriging model. The seismic response of structure is characterized by nonlinear and complexity, more difficulties in the reliability analysis have been found as well. Compared to other methods of reliability analysis, the response surface method is regarded as an effective way to solve such problems. Thus the improved response surface method based on the Kriging is utilized to analyze the structural first excursion dynamic reliability problem under random seismic excitation. Meanwhile, the influence on the reliability due to the randomness of structural parameters is analyzed.

An explicit structure-dependent algorithm for pseudodynamic testing

A novel explicit pseudodynamic algorithm is proposed for the general pseudodynamic testing, where the total response is dominated by low frequency modes while the high frequency responses are of no interest. This is because it can integrate the possibility of unconditional stability and the explicitness of each time step. In fact, it is unconditionally stable for any instantaneous stiffness softening systems, any linear elastic systems, and certain instantaneous stiffness hardening systems that might be experienced in a realistic structure. Hence, stability is not a major concern for this algorithm in practical applications. Meanwhile, it has a second order accuracy and enhanced error propagation properties. As a result, this explicit pseudodynamic algorithm is very promising for the solution of an inertia structural dynamic problem.