Search

Aims: This work is devoted to the development of a finite element algorithm for solving problem in forced vibrations of folded low shells. Methodology: The differential equations for harmonic analysis are obtained from the Lagrange variational principle. Description of the dynamic behavior is made by the structure discretization into a system of curvilinear iso-parametric finite elements used in modal analysis. The method is implemented by a calculation code on a square-plane folded shell model withnumber of crease edges in both directions k=l=3. Results: Displacement amplitudesare obtained by decomposition into vibration eigenforms. The maximum values of dynamic stresses are determined taking into account the shell's support conditions.The results of the harmonic analysis show thatimprovement in frequency characteristics and reduction of stresses in the folded shell depend on the constructive and internal damping of the structureand the increase in the number of fold edges k and l in both directions for examplebecause this contributes to decrease in the forced vibration amplitudes.

Wood fibers are industrially attractive low-cost natural materials that offer good mechanical properties. It is, however, extremely difficult to experimentally determine the elastic properties of single wood fibers due to the structural complexity and variability of basic properties. We propose a three-step finite element (FE)-modeling algorithm to predict the elastic constants of a single wood fiber. The model is based on calculating the elastic constants of the fiber in three consecutive length scales including nanostructure of cellulose microfibrils (25–30[Formula: see text]nm), ultrastructure in the fiber wall layers (2–3[Formula: see text][Formula: see text]m) and single wood fibers (30–40[Formula: see text][Formula: see text]m). The results for a given set of parameters are compared to previous studies with good agreement. The work exhibits its novelty through the model’s robustness and potential for industrial applications. It merely requires three essential inputs — chemical composition and bulk density of fiber and microfibril angle of [Formula: see text] wall layer, but is capable of predicting reasonably accurately the elastic constants of a wood fiber completely without any required model preprocessing or meshing like common commercial FE method software packages. Furthermore, the validated model is used to perform a parametric study. We have found that cellulose content has positive correlations with almost all the elastic parameters — relatively strong for [Formula: see text] and [Formula: see text], but weaker for [Formula: see text]. Lignin and hemicellulose have the greatest influence on [Formula: see text] and [Formula: see text]. The bulk density of fiber is shown to affect all elastic constants except the longitudinal elastic modulus.

We present a 2.5-dimensional (2.5-D) finite element algorithm for direct current (DC) resistivity modelling in anisotropic media with singularity removal. First, we provide the weak form of...

It is often useful to determine temperature and heat flux in multidimensional solid domains of arbitrary shape with inaccessible boundaries. In this study, an effective algorithm for solving bounda ...

In this work, we are concerned with the local and parallel finite element algorithm based on the Oseen-type iteration for solving the stationary incompressible magnetohydrodynamics. Under the uniqueness condition, the error estimates with respect to iterative step m and small mesh sizes H and $$h\ll H$$hźH of the proposed method are derived. Finally, some numerical experiments are provided to show the high efficiency of our algorithm.

The new second-order two-scale (SOTS) finite element algorithm is developed for the dynamic thermo-mechanical coupling problems in axisymmetric and spherical symmetric structures made of composite materials. The axisymmetric structure considered is periodic in both radial and axial directions and homogeneous in circumferential direction. The spherical symmetric structure is only periodic in radial direction. The dynamic thermo-mechanical coupling model is presented and the equivalent compact form is derived. Then, the cell problems, effective material coefficients and the homogenized thermo-mechanical coupling problem are obtained successively by the second-order asymptotic expansion of the temperature increment and displacement. The homogenized material obtained is manifested with the anisotropic property in the circumferential direction. The explicit expressions of the homogenized coefficients in the plane axisymmetric and spherical symmetric cases are given and both the derivation of the analytical solutions of the cell functions and the quasi-static thermoelasticity problems are discussed. Based on the SOTS method, the corresponding finite-element procedure is presented and the unconditionally stable implicit algorithm is established. Some numerical examples are solved and the mutual interaction between the temperature and displacement field is studied under the condition of structural vibration. The computational results demonstrate that the second-order asymptotic analysis finite-element algorithm is feasible and effective in simulating and predicting the dynamic thermo-mechanical behaviors of the composite materials with small periodic configurations in axisymmetric and spherical symmetric structures. This may provide a vital computational tool for analyzing composite material internal temperature distribution and structural deformation induced by the dynamic thermo-mechanical coupling response under strong aerothermodynamic environment. Second-order two-scale (SOTS) expansions for dynamic thermo-mechanical coupling problems in symmetric structure are obtained.SOTS finite element algorithm is proposed and unconditional stable implicit scheme is established.Anisotropic material is obtained by homogenization with enhanced strength and minor thermal expansion in circumferential direction.The mutual interaction and simultaneous vibration of the temperature and displacement field are simulated.A new computational tool is presented for analyzing thermo-mechanical response of composites under strong aerothermodynamic environment.

A uniaxial perfectly matched layer (PML) method is proposed for solving the scattering problem with multiple cavities. By virtue of the integral representation of the scattering field, we decompose the problem into a system of single-cavity scattering problems which are coupled with Dirichlet-to-Neumann maps. A PML is introduced to truncate the exterior domain of each cavity such that the computational domain does not intersect those for other cavities. Based on the a posteriori error estimates, an adaptive finite element algorithm is proposed to solve the coupled system. The novelty of the proposed method is that its computational complexity is comparable to that for solving uncoupled single-cavity problems. Numerical experiments are presented to demonstrate the efficiency of the adaptive PML method.

A new second-order two-scale (SOTS) analysis finite element algorithm is developed for the axisymmetric and spherical symmetric elastic problems with small periodic configurations. The axisymmetric structure considered is periodic in both radial and axial directions and homogeneous in circumferential direction, and the spherical symmetric structure is only periodic in radial direction and homogeneous in other two directions. The SOTS asymptotic expansions for the space problem, plane axisymmetric problem, and spherical symmetric problem are presented, and the main feature is that the anisotropic material is obtained by the homogenization. The analytical expressions of the cell functions and homogenized solutions for plane axisymmetric and spherical symmetric problems are obtained, and the error estimations of the expansions are established. The second-order asymptotic analysis finite-element algorithm is presented and the numerical examples are solved including the hollow cylinder, rotating disk and hollow sphere composed of periodic composite materials. The computational results demonstrate the effectiveness and accuracy of the SOTS asymptotic analysis algorithm, and the converging behavior of the asymptotic analysis algorithm agrees well with the theoretical prediction. It is also indicated that the stress distributions can be correctly computed only by adding the second-order correctors.

An adaptive finite element algorithm for problems in elastoplasticity with hardening is proven to be of optimal convergence with respect to the notion of approximation classes. The results rely on the equivalence of the errors of the stresses and energies resulting from Jensen's inequality. Numerical experiments study the influence of the hardening and bulk parameters to the convergence behavior of the AFEM algorithm. This is the first optimal adaptive FEM for a variational inequality.

This paper introduces an improved response surface-based fuzzy finite element analysis of structural dynamics. The free vibration of structure is established using superposition method, so that fuzzy displacement responses can be presented as functions of fuzzy mode shapes and fuzzy natural frequencies. Instead of direct determination of these fuzzy quantities by modal analysis which will involve the calculation of the whole finite element model, the paper proposes a felicitous approach to design the response surface as surrogate model for the problem. In the design of the surrogate model, complete quadratic polynomials are selected with all fuzzy variables are transformed to standardized fuzzy variables. This methodology allows accurate determination of the fuzzy dynamic outputs, which is the major issue in response surface based techniques. The effectiveness of the proposed fuzzy finite element algorithm is illustrated through a numerical analysis of a linear two-storey shear frame structure.

Purpose This study aims to develop an adaptive finite element method for structural eigenproblems of cracked Euler–Bernoulli beams via the superconvergent patch recovery displacement technique. This research comprises the numerical algorithm and experimental results for free vibration problems (forward eigenproblems) and damage detection problems (inverse eigenproblems). Design/methodology/approach The weakened properties analogy is used to describe cracks in this model. The adaptive strategy proposed in this paper provides accurate, efficient and reliable eigensolutions of frequency and mode (i.e. eigenpairs as eigenvalue and eigenfunction) for Euler–Bernoulli beams with multiple cracks. Based on the frequency measurement method for damage detection, using the difference between the actual and computed frequencies of cracked beams, the inverse eigenproblems are solved iteratively for identifying the residuals of locations and sizes of the cracks by the Newton–Raphson iteration technique. In the crack detection, the estimated residuals are added to obtain reliable results, which is an iteration process that will be expedited by more accurate frequency solutions based on the proposed method for free vibration problems. Findings Numerical results are presented for free vibration problems and damage detection problems of representative non-uniform and geometrically stepped Euler–Bernoulli beams with multiple cracks to demonstrate the effectiveness, efficiency, accuracy and reliability of the proposed method. Originality/value The proposed combination of methodologies described in the paper leads to a very powerful approach for free vibration and damage detection of beams with cracks, introducing the mesh refinement, that can be extended to deal with the damage detection of frame structures.

A combination method of the Newton iteration and the two-level stabilized finite element algorithm based on local Gauss integration is constructed for solving numerically the steady Smagorinsky model. This algorithm involves solving one small, nonlinear coarse mesh with mesh size H and two linear problems on the fine mesh with mesh size h . Based on the stabilized method and the Newton two-level technique, the computation will be more effective and convenient and the scaling between H and h becomes h = O ( H 4 ) , which greatly complements the results of Borggaard et al. (2008) [2] . Moreover, the stability and convergence of the two-level Newton iterative solution are analyzed. Finally, some numerical tests are made to demonstrate the effectiveness of the given method.

In this paper, we propose an adaptive finite element algorithm for the numerical solution of a class of nonlocal models which correspond to nonlocal diffusion equations and linear scalar peridynamic models with certain nonintegrable kernel functions. The convergence of the adaptive finite element algorithm is rigorously derived with the help of several basic ingredients, such as the upper bound of the estimator, the estimator reduction, and the orthogonality property. We also consider how the results are affected by the horizon parameter $\delta$ which characterizes the range of nonlocality. Numerical experiments are performed to verify our theoretical findings.

This paper presents an optimal nonconforming adaptive finite element algorithm and proves its quasi-optimal complexity for the Stokes equations with respect to natural approximation classes. The proof does not explicitly involve the pressure variable and follows from a novel discrete Helmholtz decomposition of deviatoric functions.

The nonlocal continuum dielectric model is an important extension of the classical Poisson dielectric model, but it is very expensive to be solved in general. In this paper, we prove that the solution of one commonly used nonlocal continuum dielectric model of water can be split as a sum of two functions, and these two functions are simply the solutions of one Poisson equation and one Poisson-like equation. With this new solution splitting formula, we develop a fast finite element algorithm and a program package in Python based on the DOLFIN program library such that a nonlocal dielectric model can be solved numerically in an amount of computation that merely doubles that of solving a classic Poisson dielectric model. Using the new solution splitting formula, we also derive the analytical solutions of two nonlocal model problems. We then solve these two nonlocal model problems numerically by our program package and validate the numerical solutions through a comparison with the analytical solutions. Finally, our study of free energy calculation by a nonlocal Born ion model demonstrates that the nonlocal dielectric model is a much better predictor of the solvation free energy of ions than the local Poisson dielectric model.

For second order elliptic equations with rapidly oscillating coefficients, we make some theoretical analysis for a multi-scale finite element algorithm on condition that rapidly oscillating coefficients aij belong to Sobolev spaces W1, p(Q)(1≤p

In this paper, we discuss the problem of heat exchange in composite plane wall whose heat transmitting coefficient is not a locally periodic function. For that problem, we present a method of multiscale asymptotic expansions and then propose its corresponding FE algorithm. Of course, we give comprehensive theoretical analysis for the FE algorithm. Finally, we use numerical experiments to investigate them.

Based on the full domain partition, a parallel finite element algorithm for the stationary Stokes equations is proposed and analyzed. In this algorithm, each subproblem is defined in the entire domain. Majority of the degrees of freedom are associated with the relevant subdomain. Therefore, it can be solved in parallel with other subproblems using an existing sequential solver without extensive recoding. This allows the algorithm to be implemented easily with low communication costs. Numerical results are given showing the high efficiency of the parallel algorithm.

With the wide application of complex resistivity method, searching for precise and rapid forward and inversion algorithms has become the focus of complex resistivity research. In the paper we have developed a finite element algorithm for computing the complex resistivity response of general two-dimensional models. Triangular element is used in the finite element method (FEM). The simplified boundary condition on infinite boundary is employed to improve the speed of calculation. The modeling takes two steps. Firstly, we compute apparent complex resistivity values for four different frequencies by FEM. Then, apparent Cole-Cole parameters are derived from these apparent complex resistivity values using a recursive algorithm. The algorithm has been checked with one-dimensional algorithm. Two typical two-dimensional polarization models are used by the forward approach. The apparent complex resistivity and the apparent Cole-Cole parameters maps show that there are distinct anomaly features in the pseudo-sections of apparent complex resistivity and apparent Cole-Cole parameters.

A moving mesh finite element method is proposed for the adaptive solution of second- and fourth-order moving boundary problems which exhibit scale invariance. The equations for the mesh movement are based upon the local application of a scale-invariant conservation principle incorporating a monitor function and have been successfully applied to problems in both one and two space dimensions. Examples are provided to show the performance of the proposed algorithm using a monitor function based upon arc-length.

The two-scale asymptotic (TSA) expressions of the increment of temperature and the displacement for the structure of composite materials with small periodic configuration under coupled thermoelasticity condition are derived formally in this paper, especially, the two-scale coupled relation between the increment of temperature and the displacements are set up. Then the approximate solutions and their error estimations are presented, and the multi-scale finite element algorithm corresponding to TSA is described. Finally, simple numerical results evaluated by multi-scale FE computation are shown. They demonstrate that the basic configuration and the increment of temperature strongly influence upon local strains and local stresses inside basic cell. Copyright © 2004 John Wiley & Sons, Ltd.

An algorithm based on operator splitting has been successfully implemented for solving unsteady, advection-dominated transport problems in 3-D. Specifically, the general operator-integration-factor splitting method of Maday et al. is applied to the unsteady advection–diffusion equation with source/sink terms. The algorithm incorporates a 3-D characteristic Galerkin scheme to treat advection, and a standard Galerkin treatment of the diffusion and source/sink terms. Up to third-order operator splitting was implemented and validated against several analytical solutions. The algorithm showed the expected error behaviour and good performance in modeling advection-dominated transport problems. The practical utility and effectiveness of the proposed numerical scheme was further demonstrated by solving the Graetz–Nusselt problem, i.e. high Peclet number mass/heat transport in a fully developed pipe flow.

A hybrid monotonous finite element algorithm is developed in the present paper, based on a second-order-accurate finite element scheme and a first-order-accurate monotonous one derived from the former by a unilateral lumping procedure in one dimensional case. The switch functions for the two dimensional Euler equation system are constructed locally, based on the gradient of the flow field, with special consideration on the information from neighboring elements. Examples show that the ew scheme can eliminate oscillations near strong shocks obviously.

In this paper we discuss the multiscale asymptotic expansion for a kind of general second order elliptic problem with rapidly oscillating coefficients in n-D parallelotope periodic structure. Based on the theoretical results, we investigate exhaustively the multiscale finite element algorithm. Numerical simulations are carried out to validate the proposed method of this paper.

The initial–boundary value problems in the linear theory of elasticity is considered. Based on the method of integrodifferential relations (MIDR) two dynamical variational principles is proposed and discussed. It is shown that the Hamilton principle as well as the corresponding complementary principle stated for dynamic boundary value problems follow out the variational formulations proposed. To minimize the nonnegative functional under algebraic and differential constraints a regular finite element algorithm is worked out. The algorithm allows us to estimate explicitly the local and integral quality of numerical solutions obtained. A 3D problem of lateral motions of a rectilinear elastic prism with a rectangular cross section are considered. The numerical results are presented and discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

A least square based finite element algorithm is developed for some elasto-static problems. In the formulation both stresses and displacements appear as simultaneous variables. In two dimensional (plane) analysis, parabolie isoparametric elements are used. Considerable improvement of performance is obtained with a numerical integration based on 2 × 2 Gauss point distribution over more accurate integration schemes. Reasons for this are presented. The formulation is extended in the section ‘General least square formulation’ to beams and plates with a similar success of ‘reduced’ integration.

The nonlinear diffusion equation as applied to two-dimensional time-dependent magnetic fields is solved with a finite element algorithm. This algorithm permits the analysis of problems possessing complex geometries, induced eddy currents, permanent magnets, and nonperiodic excitation currents. The numerical procedure utilizes implicit time stepping with an iterative scheme to solve the resulting set of equations. Two examples of applications of this program are presented.

Finite element algorithms for large elastic-plastic deformation are predominantly based on explicit integration of the constitutive relations on tangent stiffness form. The final stress must be corrected back to the yield surface in a somewhat arbitrary fashion.