Showing papers on "Finite element method published in 1985"

A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation

Abstract: This communication discusses a 4-node plate bending element for linear elastic analysis which is obtained, as a special case, from a general nonlinear continuum mechanics based 4-node shell element formulation. The formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate (and shell) element.

Computational Methods for Transient Analysis

Abstract: Preface. 1 . An Overview of Semidiscretization and Time Integration Procedures (T. Belytschko). 2 . Analysis of Transient Algorithms with Particular Reference to Stability Behavior (T.J.R. Hughes). 3 . Partitioned Analysis of Coupled Systems (K.C. Park and C.A. Felippa). 4 . Boundary-Element Methods for Transient Response Analysis (T.L. Geers). 5 . Dynamic Relaxation (P. Underwood). 6 . Dispersion of Semidiscretized and Fully Discretized Systems (H.L. Schreyer). 7 . Silent Boundary Methods for Transient Analysis (M. Cohen and P.C. Jennings). 8 . Explicit Lagrangian Finite-Difference Methods (W. Hermann and L.D. Bertholf). 9 . Implicit Finite Element Methods (M. Geradin, M. Hogge and S. Idelsohn). 10 . Arbitrary Lagrangian-Eulerian Finite Element Methods (J. Donea). Indices.

Fractional calculus in the transient analysis of viscoelastically damped structures

Abstract: Fractional calculus is used to model the viscoelastic behavior of a damping layer in a simply supported beam. The beam is analyzed by using both a continuum formulation and a finite element formulation to predict the transient response to a step loading. The construction of the finite element equations of motion and the resulting nontraditional orthogonality conditions for the damped mode shapes are presented. Also presented are the modified forms of matrix iteration required to calculate eigenvalues and mode shapes for the damped structure. The continuum formulation, also incorporating the fractional calculus model, is used to verify the finite element approach. The location of the poles (damping and frequency) are found to be in satisfactory agreement, as are the modal amplitudes for the first several modes.

Structural Dynamics: Theory and Computation

Abstract: Part I: structures modelled as a single degree-of-freedom system undamped single degree-of-freedom system damped single degree-of-freedom system response of one-degree-of-freedom system to haarmonic loading response to general dynamic loading Fourier analysis and response in the frequency domain generalized co-ordinates and Rayleigh's method nonlinear structural response response spectra. Part II: structures modelled as shear buildings the multistory shear building free vibration of a shear building forced motion of shear buildings damped motion of shear buildings reduction of dynamic matrices. Part III: framed structures modeled as discrete multidegree-of-freedom systems dynamic analysis of beams dynamic analysis of plane frames dynamic anaylsis of grids three-dimensional frames dynamic analysis of trusses time history response of multidegree-of-freedom systems. Part IV: structures modelled with distributed properties dynamic analysis of systems with distributed properties discretization of continuous systems. Part V: introduction to finite element method dynamic analysis of plates dynamic analysis of shells dynamic analysis of three-dimensional solid structures. Part VI: random vibration. Part VII: earthquake engineering equivolent staic lateral force method - uniform Building Code 1994 dynamic method - uniform Building Code - 1994.

An apporach to automatic three‐dimensional finite element mesh generation

Abstract: Recently developed solid modelling systems for the design of complex physical solids using interactive computer graphics offer the exciting possibility of an integrated design/analysis system. Called geometric modellers, these systems build complex solids from primitive solids (cubes, cylinders, spheres, solid patches, etc.) and macro solids (combination of primitives)3, 4, 8, 16, 18, 25, 38. To provide an effective structural analysis capability for these systems, methods must be devised to ease the burden of discretizing the solid geometry into a user controlled (usually locally graded) finite element mesh. The purpose of this paper is to describe an interactive solid mesh generation system capable of generating valid meshes of well-proportional tetrahedral finite elements for the decomposition of multiply connected solid structures. The system uses a semi-automatic node insertion procedure to locate element node points within and on the surface of a structure. An independent automatic three-dimensional triangulator then accepts these nodes as input and connects them to form a valid finite element mesh oftetrahedral elements. Although this report makes use of a modeller based on a constructive solid geometry representation (a so-called CSG modeller), the mesh generation strategy elaborated herein is completely general and makes no particular use of the CSG representation.

Energy and Finite Element Methods in Structural Mechanics

Abstract: THE FINITE ELEMENT METHOD : Basic Concepts and ApplicationsDarrell Pepper, Advanced Projects Research, Inc. California, and Dr . JuanHeinrich, University of Arizona, TucsonTh i s introductory textbook is designed for use in undergraduate, graduate, andshort courses in structural engineering and courses devoted specifically to thefinite element method. This method is rapidly becoming the most widely usedstandard for numerical approximation for partial differential equations definingengineering and scientific problems.The authors present a simplified approach to introducing the method and a coherentand easily digestible explanation of detailed mathematical derivations andtheory Example problems are included and can be worked out manually Anaccompanying floppy disk compiling computer codes is included and required forsome of the multi-dimensional homework problems.

Smeared Crack Approach and Fracture Localization in Concrete

Abstract: The possibilities of the smeared crack concept for simulating crack propagation and fracture in concrete is investigated. A smeared crack formulation is proposed which treats concrete constitutive behaviour separately from crack interface behaviour. In this study concrete is in most cases modelled as having linearly elastic characteristics. For the crack (or the band of micro-cracks) tensile-softening and shear transfer are allowed to take place but no interaction between these phenomena is taken into account. A crack closing option is included. The model has been evaluated by using the DIANA finite element package. Three types of example problems are considered. First, mode I fracture in unreinforced concrete is discussed. Emphasis is placed upon the effect of the basic concrete softening properties, such as the shape of the strainsoftening branch and the value of the fracture energy Gr. The way in which stable and mesh-insensitive solutions can be obtained is demonstrated. Next, mixed-mode fracture in unreinforced concrete is discussed. Here, the predicted post-peak response is shown to be unstable, which has to do with the existence of a considerable number of cracks of which only a limited number is active while the majority is arrested or closed. Again mesh-sensitivity of the results is examined, not only with respect to mesh refinements but also with respect to a change in the orientation of mesh lines. Very fine meshes seem to be most promising for reproducing curvilinear crack trajectories. Finally, mixed-mode fracture in two shear-critical reinforced beams is analysed, one of which fails in diagonal tension and one in shear-compression. Sudden extensive diagonal cracking is shown to be simulated quite correctly, although it should be added that corresponding genuine limit loads are not always attained. Further, comments are made on the crack shear representation adopted, involving a constant shear retention factor. The principal outcome of the project is that pronounced fracture localization can in principle be predicted by using a smeared crack strategy. However, problems are also encountered to which no definite answers can yet be given. Throughout the article possible future approaches are indicated which may help to solve them.

Analysis of laminated composite plates using a higher‐order shear deformation theory

Abstract: A higher-order deformation theory is used to analyse laminated anisotropic composite plates for deflections, stresses, natural frequencies and buckling loads. The theory accounts for parabolic distribution of the transverse shear stresses, and requires no shear correction coefficients. A displacement finite element model of the theory is developed, and applications of the element to bending, vibration and stability of laminated plates are discussed. The present solutions are compared with those obtained using the classical plate theory and the three-dimensional elasticity theory.

Non-orthogonal cracks in a smeared finite element model

Abstract: A new model for handling non‐orthogonal cracks within the smeared crack concept is described. It is based on a decomposition of the total strain increment into a concrete and into a crack strain increment. This decomposition also permits a proper combination of crack formation with other non‐linear phenomena such as plasticity and creep and with thermal effects and shrinkage. Relations are elaborated with some other crack models that are currently used for the analysis of concrete structures. The model is applied to some problems involving shear failures of reinforced concrete structures such as a moderately deep beam and an axisymmetric slab. The latter example is also of interest in that it confirms statements that ‘reduced integration’ is not reliable for problems involving crack formation and in that it supports the assertion that identifying numerical divergence with structural failure may be highly misleading.

Application of computers in fatigue analysis

Abstract: The availability of minicomputers and microprocessors, at a reasonable cost, has provided a significant stimulus in a critical appraisal of fatigue testing and analysis methods. This thesis reviews and extends some of the recent fatigue analysis methods. Two major areas investigated in detail are cycle counting methods and methods for prediction of fatigue life to crack initiation. The three recent counting methods, range-pair, Wetzel's and rainflow, which avoid the distortion and inaccuracy from which the traditional cycle counting methods suffer, are described and compared with each other to find out the similarities and differences between them. It is shown that if a service loading history starts and ends at an extreme peak, then all the three methods give an identical count. All relevant methods for the description of measured service histories are reviewed critically in connection with fatigue life assessment, service history regeneration and simulation. Confidence in the rainflow method for better fatigue life predictions and increased use of analytical methods like Finite Element analysis offering frequency domain information about a component have initiated a search for a link between rainflow counting and the power spectral density of a stationary and ergodic random process. Using a Monte Carlo approach and digital simulation techniques, the thesis presents a link in the shape of a closed-form expression which defines the probability density function of rainflow counted ranges for any given power spectral density. A closed-form expression for the distribution of ordinary ranges is also presented. Methods of predicting fatigue crack initiation life under variable amplitude loading are reviewed. From the basic ingredients of the local-strain approach, various life prediction procedures are assembled methodically with regard to how the local stress and strain are determined for a given load level, how the local stress and strain are linked to the life, and how the mean stress effect is accounted for. Predictions made by these methods are compared with the published test data; however predictions are compared mostly within themselves in order to highlight the differences between methods. It is shown that under certain circumstances, some methods give very erroneous results. A sensitivity analysis is carried out to examine how sensitive various methods are to changes in the material properties. A new procedure of determining the material properties from the experimental data is proposed.

Dynamics of Viscoelastic Structures—A Time-Domain, Finite Element Formulation

Abstract: Mathematical models of elastic structures have become very sophisticated: given the crucial material properties (mass density and the several elastic moduli), computer-based techniques can be used to construct exotic finite element models. By contrast, the modeling of damping is usually very primitive, often consisting of no more than mere guesses at “modal damping factors.” The aim of this paper is to raise the modeling of viscoelastic structures to a level consistent with the modeling of elastic structures. Appropriate material properties are identified which permit the standard finite element formulations used for undamped structures to be extended to viscoelastic structures. Through the use of “dissipation” coordinates, the canonical “M , K ” form of the undamped motion equations is expanded to encompass viscoelastic damping. With this formulation finite element analysis can be used to model viscoelastic damping accurately.

Use of Statical Indentation Laws in the Impact Analysis of Laminated Composite Plates

Abstract: The low-velocity impact response of graphite/epoxy laminates was investigated theoretically and experimentally. A nine-node isoparametric plate finite element in conjunction with an empirical contact law was used for the theoretical investigation. Theoretical results are in good agreement with strain-gage experimental data. The results of the investigation indicate that the present theoretical procedure describes the impact response of laminate for low-impact velocities.

Electrical Impedance Computed Tomography Based on a Finite Element Model

Abstract: A simulation study of electrical impedance computed tomography is presented. This is an inverse problem. A field is discretized by the finite element method and an iterative approach derived from the sensitivity theorem is examined for leads taken on the field surface. It is shown that the conductivity distribution in the field can be estimated from the impedance data obtained for the body surface leads. Simulation suggests the availability and the limitation for impedance plethysmography application. The finite element model must be chosen properly to provide the unique solution.

Finite Element Structural Analysis

Abstract: Finite Element Structural Analysis The finite element method (FEM) is a powerful technique originally developed for numerical solution of complex problems in structural mechanics, and it remains the method of choice for complex systems.In the FEM, the structural system is modeled by a set of appropriate finite elements interconnected at discrete points called nodes. Elements may have physical properties such as thickness ...

An isoparametric joint/interface element for finite element analysis

Abstract: A generally applicable and simple joint/interface element for three- and two-dimensional finite element analysis is presented. The proposed element can model joints/interfaces between solid finite elements and shell finite elements. The derivation of the joint element stiffness is presented and algorithms for the treatment of nonlinear joint behaviour discussed. The performance of the element is tested on typical problems involving shell-to-shell and shell-to-solid interfaces.

On the impact of initially stressed composite laminates

Abstract: The impact response behavior of initially stressed composite laminates is investigated using the finite element method. An experimentally established contact law is incorporated into the finite element program. The Newmark time integration algorithm is used for solving the time dependent equations of the plate and the impactor. Numerical results, including the contact force history, deflection, and strain in the plate, are presented. Effects of impact velocity, initial stress, and the mass and size of the impactor are discussed.

General Purpose Compositional Model

Abstract: A direct sequential method has been developed to simulate isothermal compositional systems. The solution technique is the same as that of the Impes method; a pressure is treated implicitly and the component masses are treated explicitly. The method handles uniformly a whole range of cases from black-oil models to compositional models of imcompressible and compressible fluid systems. The numerical solution is based on the integrated finite-difference form that allows one-, 2- and 3-dimensional grids of regular or irregular volume elements to be handled with the same ease. A concise, versatile computer program has been written in PL/I code that can easily be read, modified, and further developed. The description of the fluid system is a separate part of the model and it can easily be changed; thus, the model is highly suitable for simulating various isothermal enhanced recovery schemes such as miscible gas displacement or chemical flooding. 26 references.

Structural shape optimization with geometric description and adaptive mesh refinement

Abstract: Earlier work on shape optimization indicated that a simple problem description format was crucial to effective use of the program. As a result, a geometric problem description format which uses only boundary information was developed. A finite element mesh generation capability which requires only boundary information is used to generate the mesh, and a solution-based adaptive mesh refinement scheme is used to provide a more accurate estimate of the true solution. During the optimization process, periodic refinements are performed to generate estimates of the refined stresses based on unrefined solutions. Nonlinearities in the constraints led to some convergence difficulties; however, minimum mass designs typically were obtained in 30-40 finite element solutions.

Simultaneous analysis and design

Abstract: Optimization techniques are increasingly being used for performing nonlinear structural analysis. The development of element by element (EBE) preconditioned conjugate gradient (CG) techniques is expected to extend this trend to linear analysis. Under these circumstances the structural design problem can be viewed as a nested optimization problem. There are computational benefits to treating this nested problem as a large single optimization problem. The response variables (such as displacements) and the structural parameters are all treated as design variables in a unified formulation which performs simultaneously the design and analysis. Two examples are used for demonstration. A seventy-two bar truss is optimized subject to linear stress constraints and a wing box structure is optimized subject to nonlinear collapse constraints. Both examples show substantial computational savings with the unified approach as compared to the traditional nested approach.

Finite Element Analysis and Applications

Abstract: Preface Introduction Variational Principles Basis Functions Methods of Approximation Time-dependency Problems Convergence of Approximation Developments and Applications References Index.