Nonlinear finite element analysis

Sound knowledge of the joint behavior is required for a successful design of bonded joints. To characterize the bonded joint, the loading in the joint and the mechanical properties of the substrates and of the adhesives must be properly defined. The behavior of the bonded joint is investigated by finite element (FE) analysis methods. While for the design of large structures a cost-efficient modeling method is necessary, the nonlinear finite element methods with a hyperelastic material model are required for the detailed joint analysis. Our experience of joint analysis is presented below, and compared with test results for mass transportation applications. 

The use of this modulus based on the maximum stress in the part should provide a conservative estimate of the time and temperature dependent deflection of the part. When the isochronous stress-strain curve is highly nonlinear or the part geometry is complex, finite-element structural analysis techniques can be used. Then, the complete nonlinear, isochronous stress-strain curve can be used in a nonlinear finite-element analysis or a linear effective modulus can be used in a linear analysis. 

The estimated ultimate load of pile foundation is an important project and involves a number of challenges from the geotechnical and structural safety viewpoint. The strength reduction method of pile foundation and estimation criterion of ultimate load is studied based on nonlinear finite element and cusp catastrophe theory. The finite element limit analysis of pile is performed using the single reduction factor and two reduction factors of strength reduction method and the criterion of the cusp catastrophe curve method, and has been shown to be a reliable and objective method for estimating the ultimate load of pile. 

Andruel, R.H., Dillard, D.A. and Holzer, S.M., Two- and three-dimensional geometrical nonlinear finite elements for analysis of adhesive joints. Int. J. Adhes. Adhes., 21, 17-34 (2001). 

If FS-post >1 is calculated, ground deformations from the design earthquake are often computed for dam performance evaluation, preferably using a nonlinear finite element dynamic analysis. The Newmark sliding block deformation analysis should be avoided for computing deformations of dams involving soil hquefaction. 

A more rigorous and direct method for computing earthquake-induced ground deformations, with and without soil liquefaction, is a nonlinear finite element dynamic analysis (Finn et al. 1994) that overcomes the uncertainties associated with the approximation embedded in the pseudo-static stability calculation and in the Newmark deformation analysis. With PWP calculations built into effective stress soil models, the finite element method has the capability to simulate the coupled effects from dynamic site response, generation of excess pore water pressures, soil liquefaction, and post-liquefaction behavior, and this is a trend method for quantitative evaluation of earthquake-induced ground deformations. 

When required, combined with the use of computers, the finite element analysis (FEA) method can greatly enhanced the capability of the structural analyst to calculate displacement and stress-strain values in complicated structures subjected to arbitrary loading conditions. In its fundamental form, the FEA technique is limited to static, linear elastic analysis. However, there are advanced FEA computer programs that can treat highly nonlinear dynamic problems efficiently. 

The above problems of fabrication and performance present a challenging task of identification of the governing material mechanisms. Use of nonlinear finite element analysis enables close simulation of actual thermal and mechanical loading conditions when combined with measurable geometrical and material parameters. As we continue to investigate real phenomena, we need to incorporate non-linearities in behavior into carefully refined models in order to achieve useful descriptions of structural responses. 

The tools needed to perform such advanced analyses are not yet generally available. However, a number of commercially available finite element programs possess sophisticated nonlinear analysis capabilities. These analysis codes do not incorporate the design code checks for local member instabilities as is done in advanced analyses. In spile of this obvious and significant difference, the finite element analysis method is considered as an advanced analysis method for purposes of this report. 

Many commercial finite element computer programs (for example ABAQUS, ADINA, ANSYS, DYNA, DYNA3D, LS-DYNA, NASTRAN and NONSAP) arc readily available for nonlinear dynamic analysis. Other computer codes, such as CBARCS, COSMOS/M, STABLE, ANSR 1 have been developed specifically for the design of structures to resist blast toads. All these computer programs possess nonlinear analysis capabilities to varying degrees. 

Selected entries from Methods in Enzymology [vol, page(s)] Computer programs, 240, 312 infrared S-H stretch bands for hemoglobin A, 232, 159-160 determination of enzyme kinetic parameter, 240, 314-319 kinetics program, in finite element analysis of hemoglobin-CO reaction, 232, 523-524, 538-558 nonlinear least-squares method, 240, 3-5, 10 to oxygen equilibrium curve, 232, 559, 563 parameter estimation with Jacobians, 240, 187-191. 

In designing axi-symmetric shell structures such as large-type cooling towers, it is necessary to predict the vibration responses to various external forces. The authors describe the linear vibration response analysis of axi-symmetric shell structures by the finite element method. They also analyze geometric nonlinear (large deflection) vibration which poses a problem in thin shell structures causes dynamic buckling in cooling towers. They present examples of numerical calculation and study the validity of this method. 11 refs, cited. 

The analysis of polymer processing is reduced to the balance equations, mass or continuity, energy, momentum and species and to some constitutive equations such as viscosity models, thermal conductivity models, etc. Our main interest is to solve this coupled nonlinear system of equations as accurately as possible with the least amount of computational effort. In order to do this, we simplify the geometry, we apply boundary and initial conditions, we make some physical simplifications and finally we chose an appropriate constitutive equations for the problem. At the end, we will arrive at a mathematical formulation for the problem represented by a certain function, say / (x, T, p, u,...), valid for a domain V. Due to the fact that it is impossible to obtain an exact solution over the entire domain, we must introduce discretization, for example, a grid. The grid is just a domain partition, such as points for finite difference methods, or elements for finite elements. Independent of whether the domain is divided into elements or points, the solution of the problem is always reduced to a discreet solution of the problem variables at the points or nodal pointsinxxnodes. The choice of grid, i.e., type of element, number of points or nodes, directly affects the solution of the problem. 

A. S. Kobayashi, Dynamic Fracture Analysis by Dynamic Finite Element Method-Generation and Propagation Analysis, in Nonlinear and Dynamic Fracture Mechanics, eds. N. Perrone and S. N. Atluri, ASME, New York, 1979, pp. 19-36. 

Obviously, quantitative modelling of stress-assisted hydrogen diffusion requires the stress field in a testpiece of interest to be known. Even for rather simple cases, such as a notched bar being considered here, neither the exact solutions nor the closed form ones are usually available. Thus, one must count on some sort of the numerical solution of the mechanical portion of the coupled problem of the stress-assisted diffusion. The finite element method (FEM) approach, well-developed for both linear and nonlinear analyses of deformable solid mechanics, is a right choice to perform the stress analysis as a prerequisite for diffusion calculations. 

Some advanced general purpose finite-element codes, well adapted for stress analysis in particular, e.g. ABAQUS or MSC.MARC, have certain capabilities to simulate the stress-assisted diffusion, too. Unfortunately, they still are limited in some rather important aspects. As regards ABAQUS, this allows to perform simulations of the stress-assisted diffusion governed by equation (5) "over" the data of an accomplished solution of a geometrically and physically nonlinear stress-strain analysis, i.e., for the stationary stress field at the end of some preliminary loading trajectory, but not for the case of simultaneous transient loading and hydrogenation. 

A FEA analysis can be linear or nonlinear, but for our application nonlinear effects are significant and have to be taken into account. In a finite element analysis there are at least four primary causes of nonlinearity. 

Bonet J, Wood RD. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge Cambridge University Press, 1997. 

Nonlinear Continuum Mechanics for Finite Element Analysis by J. Bonet and R. D. Wood, Cambridge University Press, Cambridge England, 1997. This book provides an interesting discussion of many of the concepts discussed in the present chapter and includes commentary on the numerical implementation of these same concepts. 

Morman, K. N., Jr., B. G. Kao, and J. C. Nagtegaal. 1981. Finite element analysis of visoelastic elastomeric structures vibrating about nonlinear statically stress configurations. SAE paper 811309. 

Linear elastic finite element analysis Accommodates complex geometries. Rapid analysis possible. Does not account for FP nonlinearity. May underestimate strains and stresses and underestimate deformations. Good only for small strains. 

Hyperelastic finite element analysis Accommodates complex geometries. Can handle nonlinearity in material behavior and large strains. Rapid analysis possible. Standard material models available. Does not include rate-dependent behavior. Cannot predict permanent deformation. Does not handle hysteresis. Some material testing may be required. Can produce errors in multiaxial stress states. 

NONLINEAR FINITE ELEMENT ANALYSIS OF CONVECTIVE HEAT TRANSFER STEADY... 

Nonlinear Finite Element Analysis of Convective Heat Transfer Steady Thermal Stresses... 

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