Showing papers in "Engineering Computations in 1997"
TL;DR: Presents recent advances obtained by the authors in the development of enhanced strain finite elements for finite deformation problems, showing in particular a mode‐free response, while maintaining a simple and efficient (strain driven) numerical implementation.
Abstract: Presents recent advances obtained by the authors in the development of enhanced strain finite elements for finite deformation problems. Discusses two options, both involving simple modifications of the original enhancement strategy of the deformation gradient as proposed in previous works. The first new strategy is based on a full symmetrization of the original enhanced interpolation fields; the second involves only the transposed part of these fields. Both modifications lead to a significant improvement of the performance in problems involving high compressive stresses, showing in particular a mode‐free response, while maintaining a simple and efficient (strain driven) numerical implementation. Demonstrates these properties with a number of numerical benchmark simulations, including a complete modal analysis of the elements.
121 citations
TL;DR: In this article, the authors derived a formulation for spatial stress tensors and spatial material tensors of hyperelastic material, and applied the described framework to several different constitutive models based on phenomenologically and physically motivated material descriptions.
Abstract: Derives a formulation for spatial stress tensors and spatial material tensors of hyperelastic material. Looks at a class of materials with the strain energy function decomposed into a volumetric and a deviatoric part. Separate terms formulate the strain energy with respect to the invariants of the left Cauchy‐Green tensor. Stress and material tensors, which play a crucial role in the solution process of the finite element formulation, are derived solely in the current configuration. Applies the described framework to several different constitutive models based on phenomenologically and physically motivated material descriptions. Proposes a formulation for the finite element implementation of van der Waals material. Compares numerical results with experimental investigations given in the literature. For three‐dimensional finite element computations standard elements and mixed elements, based on a three‐field variational principle where displacements, the hydrostatic pressure and the dilatations are independent variables, are used.
66 citations
TL;DR: In this article, a general five-axle vehicle model was developed to study the dynamic interactions between the moving mass and the bridge structural components, and the dynamic equations of equilibrium in time were integrated using the Newmark integration scheme.
Abstract: Develops a general five‐axle vehicle model to study the dynamic interactions between the moving mass and the bridge structural components. Two‐axle, three‐axle, or four‐axle sprung loads, and the limiting load conditions such as a moving constant force, a moving alternating force, a moving unsprung mass, and combinations thereof, can be treated as special cases of the more general case presented. Further, its integration with the versatile finite element modelling has enhanced the practical applicability of such a theoretical development. The physical characteristics of the bridge and the vehicle, such as the bridge geometry, mechanical properties, profile of the road surface, the vehicle parameters including the distance between axles, leaf springs suspension and the total weight, are considered explicitly in the present model. The dynamic equations of equilibrium in time are integrated using the Newmark integration scheme. Verifies the accuracy of the algorithm by comparing the numerical results obtained from the present formulation with the experimental results.
43 citations
TL;DR: A bibliographical review of the finite element methods applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view is given.
Abstract: Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.
36 citations
TL;DR: An interpolatory subdivision scheme to generate adaptively refined quadrilateral meshes which approximate a smooth surface of arbitrary topology, which differs significantly from classical mesh generation techniques based on spline surfaces or implicit representations.
Abstract: Presents an interpolatory subdivision scheme to generate adaptively refined quadrilateral meshes which approximate a smooth surface of arbitrary topology. The described method differs significantly from classical mesh generation techniques based on spline surfaces or implicit representations since no explicit description of the limit surface is used. Instead, simple affine combinations are applied to compute new vertices if a face of the net is split. These rules are designed to guarantee asymptotic smoothness, i.e. the sequence of refined nets converges to a smooth limit surface. Subdivision techniques are useful mainly in applications where a given quadrilateral net is a coarse approximation of a surface and points on a refined grid have to be estimated. To evaluate the proposed approach, shows examples for FE‐computations on surfaces generated by this algorithm.
33 citations
TL;DR: In this paper, the evolutionary structural optimization method was extended to solve structural natural frequency optimization problems for two-dimensional structures with additional non-structural lumped masses, and two examples were given to demonstrate the feasibility of the extended EO method when used to solve SNFO problems.
Abstract: Extends the evolutionary structural optimization method to the solution for the natural frequency optimization of a two‐dimensional structure with additional non‐structural lumped masses. Owing to the significant difference between a static optimization problem and a structural natural frequency optimization problem, five basic criteria for the evolutionary natural frequency optimization have been established. The inclusion of these criteria into the evolutionary structural optimization method makes it possible to solve structural natural frequency optimization problems for two‐dimensional structures with additional non‐structural lumped masses. Gives two examples to demonstrate the feasibility of the extended evolutionary structural optimization method when it is used to solve structural natural frequency optimization problems.
25 citations
TL;DR: Two new time stepping schemes are presented, both of which are more stable than the existing standard schemes available and will allow researchers to attack more challenging problems than before.
Abstract: Direct and indirect time marching boundary element methods often become numerically unstable. Evidence of, and reasons for, these instabilities is provided in this paper. Two new time stepping schemes are presented, both of which are more stable than the existing standard schemes available. In particular, we introduce the Half‐step scheme, which is more accurate and far more stable than existing methods. This scheme, which is demonstrated on a simple crack problem for the displacement discontinuity method, can also be introduced into the direct boundary element method. Implementation of the Half‐step scheme into existing boundary element codes will allow researchers to attack more challenging problems than before.
23 citations
TL;DR: In this article, a triangular finite element for plate bending is presented, which has 15 degrees of freedom: six displacements at the corners and midside nodes and nine rotations normal to the element side, three along each element side.
Abstract: Presents the formulation of a new triangular finite element for plate bending. The element has 15 degrees of freedom: six displacements at the corners and midside nodes and nine rotations normal to the element side, three along each element side. The element is based on the Kirchhoff theory for plate bending and the shape functions are derived from a complete quartic polynomial. Presents a numerical assessment of the element, showing that the element passes the patch test and that it possesses a good converge rate. The stiffness matrix is integrated exactly.
21 citations
TL;DR: In this article, a generalization of the Z-Z criterion for discretization error estimation for time-dependent problems is presented, which limits the error due to discretisation within a prescribed value and studies of all other possible errors involved in finite element transient dynamic analysis are carried out systematically.
Abstract: Presents a method of obtaining an optimal mesh in the finite element analysis of two‐dimensional linear elastodynamic problems under transient dynamic loading, which is based on a generalization of the Z‐Z criterion for discretization error estimation for time‐dependent problems. The optimal mesh limits the error due to discretization within a prescribed value, and studies of all other possible errors involved in finite element transient dynamic analysis are carried out systematically. Also proposes methods to study and limit the modal truncation error. Numerous examples show the capabilities of the proposed methods and the importance of the optimal mesh and modal truncation error in finite element transient dynamic analysis.
20 citations
TL;DR: In this paper, the authors developed an iterative (k −L) −predictor/e −corrector algorithm for the finite element solution of turbulent flows using a (k−e) turbulence model.
Abstract: The finite element solution of turbulent flows using a (k‐e) turbulence model usually presents severe numerical difficulties. Develops an iterative (k‐L)‐predictor/e‐corrector algorithm for overcoming this and solving the (k‐e) turbulent models. The iterative scheme achieves convergence in L (length scale) which is proportional to (k1.5/e). Numerical results indicate that the developed iterative algorithm is very robust.
18 citations
TL;DR: In this article, the regions of dynamic instability of elastic beams constrained at the ends by means of translational and rotational elastic springs, using the equation of boundary frequencies, were analyzed.
Abstract: Finds the regions of dynamic instability of elastic beams constrained at the ends by means of translational and rotational elastic springs, using the equation of boundary frequencies. Obtains the diagrams showing the regions of instability of the beam, as a function of the dynamic component of the periodic forcing function and its frequency, from that equation in exact form. In this procedure inertial, stiffness and constraint characteristics of the examined system are taken into account. Presents selected applications concerning the analysed problem.
TL;DR: In this article, the co-operation of distinct discretized operators in connection with the integration of temporal evolution processes, and the iterative treatment of stationary equations of state is discussed.
Abstract: Addresses problems in mechanics and physics involving two or more coupled variables of different nature, or a number of distinct domains which interact. For these kinds of problems, considers numerical solution by the coupling of operators appertaining to the individual participating phenomena, or defined in the domains. Reviews the co‐operation of distinct discretized operators in connection with the integration of temporal evolution processes, and the iterative treatment of stationary equations of state. The specification of subtasks complies with the demand for an independent treatment on different processing units arising in parallel computation. Physical subtasks refer to problems of different field variables interacting on the continuum level; their number is usually small. Fine granularity may be achieved by separating the problem region into subdomains which communicate via the boundaries. In multiphysics simulations operators are preferably combined such that subdomains are processed in parallel on different units, while physical phenomena are processed sequentially in the subdomain.
TL;DR: In this paper, the authors developed an element technology to recover the plane stress response without any plane stress specific modifications in the large strain regime, where the essential feature of the proposed element formulation is an interface to arbitrary 3D constitutive laws.
Abstract: The objective of this work is to develop an element technology to recover the plane stress response without any plane stress specific modifications in the large strain regime. Therefore, the essential feature of the proposed element formulation is an interface to arbitrary three‐dimensional constitutive laws. The easily implemented and computational cheap four‐noded element is characterized by coarse mesh accuracy and the satisfaction of the plane stress constraint in a weak sense. A number of example problems involving arbitrary small and large strain constitutive models demonstrate the excellent performance of the concept pursued in this work.
TL;DR: In this article, the nonlinear dynamics due to rotor-stator contact is simulated using the finite element method, and a general contact finite element is developed and implemented into a powerful multibody dynamics software.
Abstract: The non‐linear dynamics due to rotor‐stator contact is simulated using the finite element method. Develops and describes a general contact finite element. By implementing this element into a powerful multibody dynamics software, different rotor global motions are analysed. Special attention is also given to determine the effects of rotation speed and friction on the rotor orbit during contact.
Cray1
TL;DR: FEM analysis has been increasingly employed to simulate sheetmetal forming processes for industrial application purposes as discussed by the authors, where finite element analysts are able to predict the occurrences of splits and wrinkles therefore they can make recommendations of changes to the die design and/or to the part design to avoid possible stamping failures.
Abstract: FEM analysis has been increasingly employed to simulate sheetmetal forming processes for industrial application purposes. From the simulation results, finite element analysts are able to predict the occurrences of splits and wrinkles therefore they can make recommendations of changes to the die design and/or to the part design to avoid possible stamping failures. The number of real die tryouts can be reduced, thus, the design cycle is shortened and manufacturing costs lowered. In the early times, application analysts were mostly concentrated on simulation of the stamping process itself starting from simple models, later running full size 3D models with large number of elements.
TL;DR: An automatic adaptive meshing scheme that is implemented in ZATILAN, a FE code developed in the Department of the Mechanical Engineering of the University of the Basque Country, and examines the versatility of this function in comparison with that of others.
Abstract: Proposes an automatic adaptive meshing scheme. Error in strain energy is directly obtained through strain energy density function (SED). Versatility of this function, in comparison with that of others, is looked at in detail. Mesh enrichment method consists of a series of h‐refinement steps and concludes with a single p‐refinement step. Adds that an examination of the accuracy of the element used in the refinement procedure is made. This scheme has been implemented in ZATILAN, a FE code developed in the Department of the Mechanical Engineering of the University of the Basque Country.
TL;DR: In this paper, a nonlinear numerical model for the computations of post-tensioned plane structures is presented, where curved prestressing tendons and reinforcing bars are embedded into the concrete and they are modelled independently of the concrete mesh using one-dimensional curvilinear elements.
Abstract: Presents a non‐linear numerical model for the computations of post‐tensioned plane structures. Generally curved prestressing tendons and reinforcing bars are embedded into the concrete and they are modelled independently of the concrete mesh using one‐dimensional curvilinear elements. Among the losses which influence the decrease in the prestress force, it is possible to compute the losses caused by friction between tendons and the concrete, the losses which result from the concrete deformation and the losses in the anchorage zone. The computation for post‐tensioned structures is organized in phases: the phase preceding prestressing (Phase I), the prestressing phase (Phase II) and the phase following prestressing (Phase III). The load is applied incrementally until failure. The model is tested on a number of examples.
TL;DR: In this article, the authors analyze several algorithms for the integration of the Jaumann stress rate and reveal that a commonly used algorithm is unconditionally unstable and only first-order objective in the presence of rotations.
Abstract: Analyses several algorithms for the integration of the Jaumann stress rate. Places emphasis on accuracy and stability of standard algorithms available in commercial and government finite element codes in addition to several other proposals available in the literature. The analysis is primarily concerned with spinning bodies and reveals that a commonly used algorithm is unconditionally unstable and only first‐order objective in the presence of rotations. Other proposals are shown to have better accuracy and stability properties. Finally, shows by example that even a consistent and unconditionally stable integration of hypoelastic constitution does not necessarily yield globally stable finite element simulations.
TL;DR: Develops a method which performs Boolean operations on two unstructured arbitrary meshes and creates a mesh of tetrahedral elements in their place to provide an interface between the remnants of the original meshes.
Abstract: Develops a method which performs Boolean operations on two unstructured arbitrary meshes Deletes the overlapping or interfering elements of two individual meshes and creates a mesh of tetrahedral elements in their place to provide an interface between the remnants of the original meshes Gives various examples where two volume meshes are joined or where a surface mesh is imposed on a volume mesh Shows, through these examples, the effects of various input parameters on the quality of the final mesh
TL;DR: Presents an implementation of the algebraic multigrid method, which can work in two ways: as pure multigrids method and as a pre‐conditioner for the conjugate gradient method.
Abstract: Presents an implementation of the algebraic multigrid method. It can work in two ways: as pure multigrid method and as a pre‐conditioner for the conjugate gradient method. Shows applications of the iterative solvers for problems in linear and non‐linear elasticity. Shows the range of possible applications with different examples with regular and non‐regular meshes and three‐dimensional problems.
TL;DR: In this paper, the authors present a robust and unconditionally stable return-mapping algorithm based on the discrete counterpart of the principle of maximum plastic dissipation, which is implemented in the formulation of the four-node isoparametric assumed-strain finite-rotation shell element employing the Mindlin-Reissner-type shell model.
Abstract: Presents a robust and unconditionally stable return‐mapping algorithm based on the discrete counterpart of the principle of maximum plastic dissipation. Develops the explicit expression for the consistent elasto‐plastic tangent modulus. All expressions are derived via tensor formulation showing the advantage over the classical matrix notation. The integration algorithm is implemented in the formulation of the four‐node isoparametric assumed‐strain finite‐rotation shell element employing the Mindlin‐Reissner‐type shell model. By applying the layered model, plastic zones can be displayed through the shell thickness. Material non‐linearity described by the von Mises yield criterion and isotropic hardening is combined with a geometrically non‐linear response assuming finite rotations. Numerical examples illustrate the efficiency of the present formulation in conjunction with the standard Newton iteration approach, in which no line search procedures are required. Demonstrates the excellent performance of the algorithm for large time respective load steps.
TL;DR: Two simple modifications of the usual iterative schemes are suggested, found to be more robust than those usual schemes which are normally used in numerical analysis of similar problems.
Abstract: Some frictional contact problems are characterized by significant variations in the location and size of the contact area occurring in the process of deformation. When this feature is combined with strongly non‐linear, path‐dependent material behaviour, difficulties with convergence of the typically used iterative processes can be encountered. Demonstrates this by analysis of press‐fit connection, a typical problem in which both of those characteristics can be present. Offers an explanation as to the possible source of those difficulties. Suggests in support of this explanation, two simple modifications of the usual iterative schemes. In spite of their simplicity, they are found to be more robust than those usual schemes which are normally used in numerical analysis of similar problems.
TL;DR: An efficiency study of different refinement procedures for the p‐version of the adaptive finite element method in two‐dimensional elasticity problems finds an optimal distribution of the nodeless degrees of freedom associated with the basic approximation parameter of the order p of the hierarchical shape functions.
Abstract: Presents an efficiency study of different refinement procedures for the p‐version of the adaptive finite element method in two‐dimensional elasticity problems. The refinement strategy, based on the estimated error in energy norm, attempts an optimal distribution of the nodeless degrees of freedom associated with the basic approximation parameter of the order p of the hierarchical shape functions. This procedure is combined with appropriate matrix‐handling techniques and equation solvers in order to achieve a solution of a given accuracy with the minimum computational resources in terms of computing time and storage. To this extent, convergence studies are performed with constant and variable adaptivity indices, with error estimators based on global and elemental approaches and with domain decomposition matrix‐handling techniques and the preconditioned conjugate gradient solver.
TL;DR: In this paper, a finite element/volume method for nonlinear aeroelasticity analyses of turbomachinery blades is presented, which uses an Arbitrary Lagrangian-Eulerian (ALE) kinematical description of the fluid domain.
Abstract: Presents a finite element/volume method for non‐linear aeroelasticity analyses of turbomachinery blades. The method uses an Arbitrary Lagrangian‐Eulerian (ALE) kinematical description of the fluid domain, in which the grid points can be displaced independently of the fluid motion. In addition, it employs an iterative implicit formulation similar to that of the Implicit‐continuous Eulerian (ICE) technique, making it applicable to flows at all speeds. A deforming mesh capability that can move the grid to conform continuously to the instantaneous shape of an aeroelastically deforming body without excessive distortion is also included in the algorithm. The unsteady aerodynamic loads are obtained using inviscid Euler equations. The model for the solid is general and can accommodate any spatial or modal representation of the structure. Determines the flutter stability of the system by studying the aeroelastic time response histories which are obtained by integration of the coupled equations of motion for both the fluid and the structure. Develops and demonstrates in 2D the formulation, which includes several corrections for better numerical stability. The cases studied include NACA64A006 and NACA0012 aerofoils and the EPFL Configuration 4 cascade. Finds the results from the numerical indicate good overall agreement with other published work and hence demonstrates the suitability of an ICED‐ALE formulation for turbomachinery applications.
TL;DR: In this paper, the authors derived the equation of motion in matrix form of a rotating cantilever beam with constant inplane base acceleration based on Hamilton's principle and the assumed mode method.
Abstract: Derives the equation of motion in matrix form of a rotating cantilever beam with constant in‐plane base acceleration based on Hamilton’s principle and the assumed mode method. Investigates the effects of varying parameters such as rotational speed of the beam, base radius, length, and internal damping of the beam on unstable regions.
TL;DR: The problem of structures’ sensitivities to prescribed displacements uncertainties through the use of fuzzy numbers is considered, and the effectiveness of the present method for a cantilever structure modelled in the case of a static finite element analysis is demonstrated.
Abstract: Considers the problem of structures’ sensitivities to prescribed displacements uncertainties through the use of fuzzy numbers. Important properties of fuzzy subsets have been studied and used to model uncertainties, and to solve the fuzzy linear system resulting from taking into account the uncertainties on prescribed displacements. Develops a computer program to allow comparisons between several structural designs checking common specifications. Demonstrates the effectiveness of the present method for a cantilever structure modelled in the case of a static finite element analysis.
TL;DR: In this paper, a boundary-directed remeshing scheme based on modular remehing technique has been proposed to reduce the errors arising in mapping of variables between old and new mesh systems.
Abstract: In metal forming, there are problems with recurrent geometric characteristics and without explicitly prescribed boundary conditions. In such problems, so‐called recurrent boundary conditions must be introduced. The present study deals with non‐steady‐state three‐dimensional finite element analysis for helical extrusion of twisted clover and trocoidal gear sections through a curved die. A boundary‐directed remeshing scheme based on the modular remeshing technique has been proposed to reduce the errors arising in mapping of variables between old and new mesh systems. The computed extrusion pressures in reaching the near steady‐state loading stage are compared with the results of the experiments as well as the steady‐state analysis. The three‐dimensional deformed pattern involving warping at the extruded end due to torsional deformation mode is demonstrated. For twisted clover and trocoidal gear sections, the twisted angle of an extruded product is smaller than that of the die, and the simpler the shape of the sections, the larger the amount of the deviation.
TL;DR: In this paper, a semi-heuristic method for automatic load incrementation, termed the adaptive arc-length procedure, is proposed, which is capable of detecting abrupt nonlinearities and reducing the increment size prior to encountering iterative convergence difficulties.
Abstract: In the inelastic stability analysis of plated structures, incremental‐iterative finite element methods sometimes encounter prohibitive solution difficulties in the vicinity of sharp limit points, branch points and other regions of abrupt non‐linearity. Presents an analysis system that attempts to trace the non‐linear response associated with these types of problems at minor computational cost. Proposes a semi‐heuristic method for automatic load incrementation, termed the adaptive arc‐length procedure. This procedure is capable of detecting abrupt non‐linearities and reducing the increment size prior to encountering iterative convergence difficulties. The adaptive arc‐length method is also capable of increasing the increment size rapidly in regions of near linear response. This strategy, combined with consistent linearization to obtain the updated tangent stiffness matrix in all iterative steps, and with the use of a “minimum residual displacement” constraint on the iterations, is found to be effective in avoiding solution difficulties in many types of severe non‐linear problems. However, additional procedures are necessary to negotiate branch points within the solution path, as well as to ameliorate convergence difficulties in certain situations. Presents a special algorithm, termed the bifurcation processor, which is effective for solving many of these types of problems. Discusses several example solutions to illustrate the performance of the resulting analysis system.
TL;DR: Achieves efficient structural optimization of plate structures while the design constraints are multiple frequency constraints and reduces the computational cost of optimization by approximating the frequencies using the Rayleigh quotient.
Abstract: Achieves efficient structural optimization of plate structures while the design constraints are multiple frequency constraints. Reduces the computational cost of optimization by approximating the frequencies using the Rayleigh quotient. Uses an optimality criteria method to solve each of the approximate problems. The creation of a high quality approximation is the key to the efficiency of the method. Also, with the great number of design variables, the optimality criteria methods are robust approaches. Thus the combination of approximation concepts and optimality criteria methods forms the basis of an efficient tool for optimum design of plate structures with frequency constraints. Presents examples and compares the results with previous work.
TL;DR: Demonstrates how multibody systems containing both rigid and deformable components can be handled with the aid of Autolev, a symbol manipulator for dynamics, when such components are discretized by a Rayleigh‐Ritz procedure.
Abstract: A number of computer codes are available for the automatic generation of the equations of motion of multibody systems formed by rigid bodies. Systems containing deformable components generally cannot be treated readily by these programs. Demonstrates how multibody systems containing both rigid and deformable components can be handled with the aid of Autolev, a symbol manipulator for dynamics, when such components are discretized by a Rayleigh‐Ritz procedure. A computer code called Ritz was written to perform this task interactively with Autolev, and a Fortran program is generated automatically for the numerical simulation of motions of the system under consideration. The numerical results are then converted to Matlab format, so that plotting routines and other facilities available in Matlab can be used to process the results further.