Large displacement analysis of plates by a stress-based finite element approach

A mixed-hybrid incremental variational formulation, involving orthogonal rigid rotations and a symmetric stretch tensor, is proposed for finite deformation analysis of thin plates and shells. Isoparametric eight-noded elements are based upon the Kirchhoff-Love hypotheses, the assumption of plane stress, and the moderately large rotations of Von Karman plate theory. Semilinear elastic isotropic material properties are assumed, and the right polar decomposition of the deformation gradient is used. The symmetrized Biot-Luré (Jaumann) stress measure gives a unique complementary energy density and a set of variational principles with a priori satisfaction of linear momentum balance, a posteriori angular momentum balance, and interelement traction reciprocity by means of Lagrange multipliers. The incremental modified Newton-Raphson solution procedure is generated by a truncated Taylor series expansion of the functional in a total Lagrangian formulation. The theory is applied to laterally loaded and buckled thin plates, and numerical results are compared with truncated series solutions.     

On the stress computation in finite element models based upon displacement approximations

A brief review of the various methods for the stress computation in finite elements by displacement approximation is given. Using the equilibrium equations in the nodal points, the stress resultants are obtained. A relation between these stress resultants and the distributed stresses is established with the help of the principle of virtual displacements. The so developed method may be called equilibrium-method for the stress computation. Various examples are calculated. A considerable accuracy of the results is obtained with a small number of elements.     

A finite element large displacement analysis of stiffened plates

A finite element analysis of the large deflection behaviour of stiffened plates using the isoparametric quadratic stiffened plate bending element is presented. The evaluation of fundamental equations of the stiffened plates is based on Mindlin's hypothesis. The large deflection equations are based on von Kármán's theory. The solution algmrithm for the assembled nonlinear equilibrium equations is based on the Newton-Raphson iteration technique. Numerical solutions are presented for rectangular plates and skew stiffened plates.     

Homogenization-based finite element analysis of unidirectional composites by classical and multiresolutional techniques

Computational studies of unidirectional transient problems in multiresolutional periodic heterogeneous media using homogenization technique and the finite element method are documented below. This homogenization method, being the extension of the classical two-scale asymptotic approach and based on the wavelet representation for composite parameters, is used here to calculate effective material parameters of a composite. Efficiency of this method is compared against asymptotic homogenization technique and simple spatial averaging of material properties using the FEM solution for some transient heat transfer and free vibration problems. On the other hand, a comparison with the solutions obtained for a multiresolutional decomposition of material parameters for composites is also made. Numerical results show that the homogenized parameters resulting from the new approach are bounded by spatial averages and by asymptotic method results; this result is valid also for the eigenvalues of a periodic and simply supported composite beam. The multiresolutional homogenization proposed appears to be especially efficient in case of smaller numbers of periodicity cells in the structure, while increased number of cells needs application of an asymptotic homogenization method. Further computational studies are necessary in this area, but the application of the multiresolutional technique is natural because of multiscale character of composites. Moreover, this method may be very efficient in common symbolic-FEM programs implementation.     

Thermal stress analysis of skew plates by finite element method

Thermal stresses are induced in general due to nonuniform temperature distribution or due to the boundary restriction. Most of the work reported so far deals with either plates with edges clamped in plane of the plate or plates with stress free edges. While studying buckling or post-buckling problems, one should ideally analyse the plates with mixed in-plane boundary conditions. Hence, in the present analysis, thermal stress analysis of skew plates with mixed in-plane boundary conditions using finite element approach is attempted. In addition, the effect of in-plane boundary conditions on the thermal stresses is also discussed.     

基于移动有限元法的裂纹梁振动分析

采用移动有限元法和局部柔度法对移动质量作用下含裂纹简支梁进行了振动计算分析.计算考虑了裂纹和移动质量的相对位置对梁固有频率的影响,以及移动质量在不同位置、速度情况下对裂纹梁的动力响应的影响.结果分析表明,裂纹与移动质量的存在会使得梁的动态位移有不同程度的增大,且随着移动质量位置和裂纹位置的改变会使得梁的固有频率变小.     

Numerical techniques for plasticity computations in finite element analysis

Common numerical techniques for plasticity computations in finite element analysis are examined. The plasticity theory considered is the simple rate-independent von Mises criterion for small strains. Work hardening is represented by a general isotropic model or by a linear, isotropic-kinematic mixed model. Algorithms to integrate the rate equations, strategies for stress updating over a time (load) step in implicit codes, and tangent operators consistent with the integration algorithm are discussed. The elastic predictor-radial return algorithm and a consistent tangent operator satisfy the requirements for a stable, accurate and efficient numerical procedure. An extension of this model for plane stress with mixed hardening is described. Two numerical examples are given to demonstrate the accuracy and efficiency for plane stress analyses.     

Application of multiple objective optimization techniques to finite element model tuning

This report examines tuning a finite element model using vector optimization techniques. Structural models using finite element theory often need to be adjusted so they can accurately simulate the real structure. The goal is to tune the model such that it will reproduce data derived from structural tests. First, the performance indices are extremized using multiple objective optimization theory, producing a set of possible solutions. Next, the solutions are rank ordered according to a decision maker's preferences to select the best answer. The tuning process was applied to a T-38 horizontal stabilizer. Numerous weighted solutions contained a best static deformation model, a best frequency model and three intermediate combinations of these two models. This automated procedure proved to be a versatile method capable of producing solutions for many types of tuning problems.     

Flexural analysis of reinforced fibrous concrete members using the finite element method

A numerical procedure based on the finite element method is developed for the geometric and material nonlinear analysis of reinforced concrete members containing steel fibres and subjected to monotonic loads. The proposed procedure is capable of tracing the displacements, strains, stresses, crack propagation, and member end actions of these structures up to their ultimate load ranges. A frame element with a composite layer system is used to model the structure. An iterative scheme based on Newton-Raphson's method is employed for the nonlinear solution algorithm. The constitutive models of the nonlinear material behaviour are presented to take into account the nonlinear stress-strain relationships, cracking, crushing of concrete, debonding and pull-out of the steel fibres, and yielding of the reinforcement. The geometric nonlinearity due to the geometrical change of both the structure and its elements are also represented. The numerical solution of a number of reinforced fibrous concrete members are compared with published experimental test results and showed good agreement.     

An efficient two grid method for miscible displacement problem approximated by mixed finite element methods

In the paper, we present an efficient two grid method for the miscible displacement problem which discretized by mixed finite element methods for the pressure equation and concentration equation at the same time, and then analyzed the error estimate of the two-gird algorithm. At last, the numerical experiment presented confirmed the theoretical results. Compared with the standard mixed finite element methods, this two-grid scheme based on the mixed methods can keep the same convergence order and cost much less work.     

On finite element large displacement and elastic-plastic dynamic analysis of shell structures

Finite element procedures for nonlinear dynamic analysis of shell structures are presented and assessed. Geometric and material nonlinear conditions are considered. Some results are presented that demonstrate current applicabilities of finite element procedures to the nonlinear dynamic analysis of two-dimensional shell problems. The nonlinear response of a shallow cap, an impulsively loaded cylindrical shell and a complete spherical shell is predicted. In the analyses the effects of various finite element modeling characteristics are investigated. Finally, solutions of the static and dynamic large displacement elastic-plastic analysis of a complete spherical shell subjected to external pressure are reported. The effect of initial imperfections on the static and dynamic buckling behavior of this shell is presented and discussed.     

Fatigue analysis by local stress concept based on finite element results

The assessment of finite element results for dynamically loaded components requires local S/N-curves, which depend, under further effects, on the type of loading and the stress flow within the component. These influences are described with help of the stress gradient, which can easily be determined with finite element calculations. A model for the calculation of S/N-curves is presented, which takes into account the stress gradient to define the local stress limit, the number of cycles at the fatigue limit and the slope.     

Adaptive finite element methods for shape optimization of linearly elastic structures

Grid adaptive methods combined with means for automatic remeshing are applied to problems in shape optimal design of linearly elastic structures. The quantitative effect of element distortion near the design boundaries is identified in terms of interpolation error associated with the finite element discretization. The grid adaptation is itself formulated as a structural optimization problem, with an objective function that reflects the discretization error. A ‘necessary condition’ from this formulation provides the basis for a computational procedure to predict the modified grid.To avoid the sometimes drastic distortion of the FEM grid that might otherwise occur in conjunction with design change, remeshing must be performed at intermediate stages of the overall solution process. In order to produce results for the optimal shape design without interruption in this process, the computer program combines numerical grid generation and automatic remeshing with the grid adaptation and design change. Results for several shape design problems obtained with the use of grid adaptation are compared to computational results predicted from a fixed grid. Both ‘r-’ and ‘h-adaptation’ are tested.     

The use of the Hoffman yield criterion in finite element analysis of anisotropic composites

A return mapping algorithm has been developed for the Hoffman yield function of anisotropic plasticity. The accuracy of the algorithm has been assessed by means of iso-error maps for trial stress increments in the deviatoric and volumetric plane. A tangent operator that is consistent with the developed integration algorithm has been formulated. The Hoffman model has been applied to a plate structure and to two shell structures.     

The solution of the transonic equation by optimal control and finite element methods

The transonic equation for compressible potential flow has previously been solved using the finite element method in conjunction with an optimal control algorithm. However, the method is complex and computation time is high. In this paper, by using a different performance index in the optimal control algorithm, the computation time can be significantly reduced. A numerical example is given in which the computation time is four times shorter than that using the previous method.     

Thermoelastic stress analysis of anisotropic composite sandwich plates by finite element method

In the present work a finite element approach is established for the analysis of sandwich plates with different anisotropic composite facings due to aerodynamic and thermal fields. The main contribution of this study is the consideration of the inherent coupling phenomenon of stretching and bending in such non-symmetric composite sandwich plates. Consequently, the stiffness matrix includes now sub-matrices which relate the “generalized” transverse thermal (or aerodynamic) loads to the in-plane displacements, and the in-plane forces to the “generalized” transverse displacements. These sub-matrices do not exist in symmetrically layered sandwich plates and their inclusion in the analysis is shown to be of primary importance. Three examples are included, indicating the sensibility of the stress and displacement fields to the class of heterogeneity and anisotropy of the considered sandwich plates.     

The use of finite element techniques for calculating the dynamic response of structures to moving loads

This paper presents a technique for using standard finite element packages for analysing the dynamic response of structures to time-variant moving loads. To illustrate the method and for validation purposes, the technique is first applied to a simply supported beam subject to a single load moving along the beam. Finally, it is applied to the problem that initiated the work: calculation of the effects of two-dimensional motion of the trolley on the response of the base structure of a mobile gantry crane model.     

Automated optimization of transverse frame layouts for ships by elastic-plastic finite element analysis

This paper presents a model for the optimum design of ship transverse frames. An elastic-plastic finite element analysis algorithm for plane frames has been incorporated in the model to evaluate the ultimate strength of the overall frame, and different effects of design loads. Using these strengths and load effects, appropriate design constraints are then formulated to prevent different failure categories; the overall collapse, ultimate limit state failures and serviceability failures. Possible instabilities and effects of combined loads are accounted for in formulating these constraints. Scantlings of the frame structure have been modelled as free design variables. The weight function and different constraint functions are then derived relating design variables in such a way that once parameters for finite element analysis are input, the scheme automatically forms the objective function and all constraints, and then interacts with the simplex algorithm through sequential linearization to find the optimum solution. Thus the scheme is almost automatic. Different layouts of the frame structure have been designed by executing this scheme, which demonstrates the capability of the model and the possibility of weight savings by choosing the appropriate layout. Finally, it is suggested how this model would interact with the design of longitudinal materials to ensure the overall optimality in ship hull module design, to prevent grillage buckling and to validate underlying assumptions in analysis.     

Some reflections on elastoplastic stress calculation in finite element analysis

The set of stress invariants (J₁,J'₂,θ) is very frequently employed in finite element programs for elastoplastic analysis. Some precautions are however required when computing the stress states of contact with the yield surface. The numerical problems that may arise and simple measures to avoid them are described in this paper.