General Finite Element Analysis Research Articles

Simplified method based on the deformation theory for structural limit analysis—I. Theory and formulation

Based on the deformation theory of linear hardening materials, a simplified finite element analysis method is proposed to calculate the limit load of structures. Compared with the general elasto-plastic incremental finite element analysis, the proposed method can avoid the incremental iteration of nodal displacements and the constitutive equation integration at each Gauss integral point. Compared with the mathematical programming method combined with finite element analysis, the proposed method shows theoretical simplicity and avoids bringing in complex mathematical theories. It is also easy to put into code. Compared with some current limit analysis methods, such as the GLOSS R-Node method and the elastic compensation method, the present method gives a remarkably accurate estimation of limit loads instead of just a simple lower or upper bound. Numerical examples have demonstrated that it is effective and the computational results are accurate enough to meet the need of engineering practice.

FINITE ELEMENT METHOD FOR GRADIENT PLASTICITY AT LARGE STRAINS

A finite element method for gradient elasto-plastic continuum in which the yield strength of strain hardening/softening materials not only depends on the effective plastic strain but also on its Laplacian is presented. The consistent integration algorithm to update the stress and the internal state variable at integration points and the consistent compliance matrix for the gradient plasticity are formulated in the non-local sense. The methodology to derive the finite element formulation for the gradient plasticity at large strains presented in this paper is applicable to general finite element analysis; the formulation in the context of the two-dimensional four-noded mixed finite element with one integration point and mean von Mises yield criterion is particularly derived. Numerical examples are tested to demonstrate the capability and performance of the present finite element method at large strain in solving for the strain localization problem.

Numerical analysis of the radiated fields of ultrasonic transducers

A finite element model is implemented for simulating the radiated fields of both planar and curved transducers in acoustic media. The approach is based on general finite element analysis developed for solving the governing equations of elastic wave propagation. The distributions of the wave fields are presented for both the nearfield and farfield regions of the transducer. Three excitation pulses with the same center frequency but different bandwidths are examined and the accuracy is indicated by a comparison of the simulation results for the axial and transverse fields with the analytical results for continuous wave excitation.

Simplified method for elasto-plastic finite element analysis of hardening materials

Based on the deformation theory of linear hardening materials, a simplified finite element analysis method is proposed to calculate elasto-plastic responses of general hardening materials. Compared with the general elasto-plastic incremental finite element analysis, the proposed method can avoid the incremental iteration of nodal displacements and the constitutive equation integration at each Gauss integral point. This method appears to be more theoretically reasonable, and the material property need not be limited to linear hardening. The method provides an effective tool to calculate structural elasto-plastic responses. Numerical examples have demonstrated that its computational efficiency is very much higher than that of the incremental elasto-plastic finite element analysis, and computational results are accurate enough to meet the need of engineering practice.

The criteria for identifying the type of critical points

It is well known that the buckling of a structure includes two kinds of different physical phenomena. One is called snap-through buckling and the other is called bifurcation. In this paper, the criteria to identify the two different unstable types are developed. The analysis in the present paper shows that the type of critical points can be directly determined by the incremental equilibrium equations in the general finite element analysis and that it only depends on whether or not the load increment does work through the unstable mode associated with the critical load.

Forthcoming papers

This paper presents a nonlinear time-dependent computational model for analyzing the quasistatic response of viscoelastic–viscoplastic frictional contact problems. Both material and geometrical nonlinearities are considered in the framework of the Lagrangian description. The material nonlinearity is due to the time–stress-dependency of the constitutive equation, while the geometrical nonlinearity is due to large displacements and rotations, but small strains. The model is derived based on an implicit time-integration method within a general displacement-based finite element analysis. The nonlinear Schapery’s single integral model is used to model the viscoelastic part, while the Perzyna model is adopted model the viscoplastic part. The exponential form of the Prony series is used to represent the transient component of the viscoelastic creep compliance, since it permits hereditary effects to be computed recursively. In addition, an incremental form of the viscoplastic strain component is derived in the framework of associative viscoplasticity based on implicit integration scheme. Throughout the contact interface, friction is simulated using a local-nonlinear friction law, while the Lagrange multiplier method is adopted to model the inequality contact constraints. In a presented case study, the complete contact configuration and internal stresses are analyzed. Results show the significant effects of material nonlinearity, viscoplastic flow, and friction on the response of contact problems.

A dynamical study of the proposed Space Station type configuration

The planar libration-vibration interaction dynamics of the proposed Space Station is studied using a simplified model where the keel and solar panels are represented as beams and the central pressurized modules as a rigid body. In the beginning, the governing nonlinear, nonautonomous and coupled equations of motion are derived using the classical Lagrangian procedure. This is followed by a relatively general finite element analysis of the structure to arrive at the first seven system modes and associated frequencies. Next, a parametric analysis is undertaken, through numerical integration of the equations of motion in conjunction with the modal discretization, to assess the librational and vibrational response of the system. Finally, a closed form-solution of the simplified nonlinear problem is attempted using the variation of parameters (Butenin) method. Its validity is assessed through comparison with the numerical results over a range of system parameters and initial conditions. Results provide information pertaining to the levels of librational and vibrational response and associated acceleration fields, which may prove helpful in appropriately locating experiments and monitoring instruments. It may also aid in the planning of the control system. The analytical approach provides surprisingly close correlation with the more elaborate numerical procedure, thus promising a better physical appreciation of the complex interactions as well as a considerable saving in the computational cost.

Analysis of a High-Speed Flexible Four-Bar Linkage: Part II—Analytical and Experimental Results on the Apollo

By using the equations of motion derived from the virtual displacement [1], a general finite element analysis computer code FEMAP (Four-bar Elastic Mechanism Analysis Program) for the planar motion is developed on the Apollo computer. The output of this program includes the following analysis for any point in the mechanism: velocity, acceleration, natural frequency, displacement, stress and strain. The displacement, stress and strain can be either quasi-static or full vibration analysis. The animation of the entire motion of the flexible linkage can be displayed on the screen. Analytical results are compared with results from a new experimental method which combines high-speed photography with a digital image processing technique.

Analysis of a High-Speed Flexible Four-Bar Linkage: Part I—Formulation and Solution

Derived from the principle of virtual displacement, a general finite element analysis computer code (FEMAP) of the flexible four-bar linkage is developed on the Apollo computer. In this part, virtual displacement method is presented as a basic theory for the general formulation of the equations of motion. Based on these results, a general finite element computer code of planar four-bar linkage is developed. All the links of the mechanism are considered to be flexible. The nonlinear terms such as coupling between the rigid body and elastic deformation terms and the effect of the axial forces are included. The Newmark direct integration method is used as solution scheme.

Layering of RC Membrane and Plate Elements in Nonlinear Analysis

Use of a layering technique in general nonlinear finite element (FE) analysis of reinforced‐concrete flat shell elements is introduced. Stack of simple four‐node plane stress and Mindlin plate elements is used to simulate RC elements subjected to membrane and bending loads. Transverse shear deformations are taken into account and compatibility between layers is satisfied by means of nodal constraint equations. The method along with nonlinear constitutive models for concrete and steel are implemented in a FE program. Efficient stiffness calculation, assembly, and solution algorithms are employed to minimize the computational effort. Experimental specimens are analyzed. The results indicate the effectiveness and efficiency of the layering technique in simulating the behavior under membrane as well as flexural loading cases. The provided flexibility in the thickness direction makes it possible to model transverse shear deformations and to simulate bond degradation between concrete and steel. The importance o...

Postbuckling behavior of selected curved stiffened graphite-epoxy panels loaded in axial compression

Results of an experimental and analytical study of the postbuckling behavior of selected curved stiffened graphite-epoxy panels loaded in axial compression are presented. The postbuckling response and failure characteristics of the panels are described. Each panel had four equally-spaced I-shaped stiffeners and 16-ply quasi-isotropic skins. Panels with three different stiffener spacings were tested. Failure of all panels initiated in a skin-stiffener interface region. Analytical results from a nonlinear general shell finite element analysis computer code correlate well with typical postbuckling test results up to failure. The analytical modeling detail necessary to predict accurately the response of the panel is described. Measured initial geometric imperfections were included in the postbuckling analysis.

Effective stress analysis of seismic site response

AbstractA procedure is presented which allows site response analyses to be performed with any general multidimensional finite element analysis package. Numerical results which corrorate the theory are presented. Also, as an illustration of the procedure, results of an effective stress analysis for the scismic response and liquefaction of a horizontally layered saturated sand deposit are presented.

Shape optimization of three-dimensional folded-plate structures

The basic features of a previously described shape optimization capability included a general geometric problem description format and adaptive finite element analysis. The finite element mesh for each design step was created from the boundary information only and refined using finite element solution results. At that time, only structures in a single plane could be treated. This work has now been extended to handle structures created from an assembly of segments that may be rotated into any plane as well as to contain the nonplanar surface curvature within any segment. In order to handle these more general problems, it was necessary to introduce a more efficient mesh generation scheme. Several design examples are presented to demonstrate each of the features.

Postbuckling behavior of selected flat stiffened graphite-epoxy panels loaded in compression

Results of an experimental study of the postbuckling behavior of selected flat stiffened graphite-epoxy panels loaded in compression are presented. The postbuckling response and failure characteristics of undamaged panels and panels damaged by low-speed impact are described. Each panel had four equally-spaced I-spaced stiffeners and 16- or 24-ply quasi-isotropic skins. Panels with three different stiffener spacings were tested. Some undamaged specimens supported as much as three times their initial buckling load before failing. Failure of all panels initiated in a skin-stiffener interface region. Analytical results obtained from a nonlinear general shell finite element analysis computer code correlate well with typical postbuckling test results up to failure. The analytical modeling detail necessary to predict accurately the response of a panel is described. Test results show that low-speed impact damage can reduce the postbuckling strength of a stiffened panel and that the skin-stiffener interface region is more sensitive to impact damage than the skin midway between stiffeners.

Finite-element analysis of a porous thrust slider

A general finite-element analysis is presented for solution of the flow field equations for porous bearing lubrication considering tangential velocity slip in accordance with the Beavers-Joseph criterion. Expressions for load support and friction are included and the analytical procedure for computing fluid film stiffness and damping for a thrust slider is explained. The numerical results for a porous step slider were obtained for a wide range of design parameters which control the tangential velocity. The effect of velocity slip on the porous step slider performance is discussed and explained with reference to velocity profiles across the film.

A design scheme for ship structures : Smith, G. K. and Woodhead, R. G.The Royal Inst. of Naval Archit. Spring Meeting 1973 (April 1973), 12 pages

The development of a design system capable of application to large complex ship structures is described. In broad terms the computer based system consists of a general automatic finite element analysis model linked to an optimisation routine. The key areas discussed in the paper are the mathematical modelling of design problems, the use of finite element method in design and the efficient optimisation of large design problems. An explanatory example is given and full results from an application of the system to the design of a tanker transverse are presented. /AUTHOR/