Three‐Dimensional Finite Element Analysis in Airport Pavement Design

This paper discusses work being performed at the Federal Aviation Administration (FAA) Airport Technology R&D Branch in the development of a three‐dimensional finite element‐based airport pavement design procedure for rigid airport pavements. The structure of the pavement design procedure and the function of the finite element structural model within it are described. A major focus of current FAA research and development efforts is on reducing run time. A simplified, single‐slab mesh runs on a personal computer and returns a maximum edge stress in a fraction of the time required by the full nine‐slab mesh. Results are presented for the simplified mesh for various aircraft types and slab sizes and compared to the larger mesh. Two types of foundation models are considered to represent a subgrade of infinite depth. A subgrade model consisting of discrete springs at nodal points approximates the distributed spring (Winkler) foundation with subgrade modulus k used in Westergaard analysis. An alternative model makes use of infinite elements to represent a linear elastic foundation with elastic modulus E and Poisson’s ratio μ. Stress computations using both models show that the Winkler foundation model is significantly more sensitive to slab size than the infinite element model for dual‐tridem (six‐wheel) aircraft gear loads. In a recent project at the FAA Center of Excellence (COE) for Airport Pavement Research, the open source code software (Nike3D) used in the three‐dimensional finite element computations to include the infinite element formulation. The infinite element was implemented as a new material type applicable to standard eight‐node elements in the Nike3D element library.     

Finite-Element Analysis of Tapered Steel and Fiber-Reinforced Plastic Bridge Camera Poles

This paper presents experimental and finite element investigations of the load-deformation behavior of tapered steel and fiber-reinforced plastic (FRP) bridge camera poles subjected to cantilever bending type loading. Three full-scale experimental tests are conducted on one tapered octagonal steel cross section and two FRP circular cross-section poles to identify their load deformation characteristics. Three-dimensional isoparametric finite-element models of the poles are developed by considering the nonlinear coupling behavior between material, contact, and geometric effects. The elastoplastic solid elements with eight nodes are employed for the effective three-dimensional finite-element modeling and analysis. A surface-to-surface contact algorithm is used to simulate the interaction between contact surfaces. An energy-based convergence criterion is adopted to obtain the converged coupled nonlinear solutions. The obtained load-deformation results from finite-element analyses are compared with those of the experiments. The behavior of the finite-element models is examined by observing the effects of individual geometric variables on the load-deformation characteristics of the poles.     

Alternative Approach to Modify a Discrete Kirchhoff Triangular Element

In this paper, the existing modified discrete Kirchhoff triangular bending element is further modified, using the least-squares method, to enable the analysis of arbitrary thin plate with different material and geometric properties. In the vibration and buckling analyses, the combined mass and combined geometric stiffness matrices are employed to improve the calculations of natural frequency and buckling load. A comparison between the proposed element and some existing elements shows that the former is a high precision element for thin plate bending, vibration, and buckling analyses.     

Adaptive Refinement/Recovery for Analysis of Wind around Structure

For the efficient finite-element wind analysis, using the optimal mesh is one of the most important factors. The optimal mesh can be obtained when the errors of the solution are distributed uniformly over the entire domain. The study presents the development of a transition element for flow analysis, an element that has a variable number of midside nodes and can be effectively used in the adaptive mesh refinement by connecting the locally refined mesh to the existing coarse mesh through a minimum mesh modification. In the dynamic analysis of flow, the optimal mesh should be changed continuously in accordance with the changing error distribution; the proposed refinement/recovery scheme was found to be very effective for this purpose. The modified superconvergent patch recovery for the variable-node element is presented to estimate a posteriori error of the solution for the adaptive mesh refinement. The boundary conditions of the nodes generated by refinement process are different from those used in the ordinary finite-element method, in order to describe the singular point correctly. The numerical examples show that the optimal mesh for the finite-element analysis of flow around the structures can be obtained automatically by the proposed scheme.     

A Study of Nonlinear Tire Contact Pressure Effects on HMA Rutting

The Indiana Department of Transportation/Purdue University accelerated pavement testing (APT) facility has been utilized in a number of studies of hot mix asphalt (HMA) rutting performance. The benefit of using APT is that rutting performance can be established in a few days of testing. Finite element (FE) models have been developed for relating APT to in‐service pavement performance. Factors addressed in the models include pavement geometry, boundary conditions, materials, loads, test conditions, and construction variables. Determining the effects of these factors provides a means for better interpreting APT test results and HMA rutting performance. A detailed analysis using 3D and 2D FE has been made of tire/pavement contact pressure effects on rutting. The analyses include tread pattern and constant and varying contact pressure. A creep model is used to represent the HMA time‐dependent material behavior. Based on test data, the material constants in the creep model were back calculated. Results of the FE studies show that the creep model can successfully characterize pavement material behavior through a reasonable approximation of loading and other factors.     

Application of Graded Finite Elements for Asphalt Pavements

Asphalt paving layers, particularly the surface course, exhibit vertically graded material properties. This grading is caused primarily by temperature gradients and aging related stiffness gradients. Most conventional existing analysis models do not directly account for the continuous grading of properties in flexible pavement layers. As a result, conventional analysis methods may lead to inaccurate prediction of pavement responses and distress under traffic and environmental loading. In this paper, a theoretical formulation for the graded finite element method is provided followed by an implementation using the user material subroutine (UMAT) capability of the finite element software ABAQUS. Numerical examples using the UMAT are provided to illustrate the benefits of using graded elements in pavement analysis.     

Active Control of Structures in Nonlinear Response

The need to account for geometric and material nonlinearities in the active control of highly flexible, large, space structures is emphasized herein. The performance index of the control problem is minimized subject to equations of state and costate using a variable metric algorithm. Unlike the conventional techniques for active control, the present algorithm is able to exploit the sparsity and symmetry of the mass and stiffness matrices of the finite element models of structures. The algorithm thus has the potential of being able to control moderately large‐scale, finite element models of highly flexible, large, space structures in a cost‐effective manner. The proposed algorithm is validated in suppressing the nonlinear vibrations of an impulsively loaded, highly flexible beam, and the need for inclusion of nonlinearities is demonstrated.     

Displacement-Based and Two-Field Mixed Variational Formulations for Composite Beams with Shear Lag

Displacement-based and two-field mixed beam elements are proposed for the linear analysis of steel–concrete composite beams with shear lag and deformable shear connection. The kinematics of the shear lag relies on a parabolic shear warping function of uniform shape along the slab. These assumptions are verified by comparing a closed-form solution of the composite beam problem with the results provided by the ABAQUS code. Moreover, three displacement-based finite elements and two mixed elements where both variables, forces, and displacements are approximated within the elements are developed especially for very coarse discretizations. All models neglect uplift and consider shear connectors using distributed interface elements. Locking problems that arise in the 10 degrees-of-freedom (DOF) displacement-based element which ensures the lowest regularity required by the problem are detected. Then, a locking-free element which relies on a reduced integration and a scaling factor method is proposed and analyzed for fine mesh discretizations. Energy errors and convergence rates of the proposed elements are illustrated while numerical examples dealing with a fixed-end steel–concrete composite beam and a simply supported concrete Tee beam are considered to confirm the validity of the closed-form solution and illustrate the performance of the proposed elements, especially of the ones with 10 and 13 DOF.     

Continuum Modeling of an Innovative Space-Based Radar Antenna Truss

Many proposed inflatable designs for space applications consist of truss-like or lattice structures due to their simplicity of construction coupled with large stiffness to density ratios. An analytical approach is presented here in order to derive the governing partial differential equations of motion which are decoupled for bending and rotational coordinates of vibrations and applies this formulation to the truss structure model of an innovative space-based radar antenna. Kinetic and potential energy expressions are written in terms of nodal velocities and strain components of bar members within a repeating truss element. Hamilton’s principle is then employed to find the equations of motion for the system. The equations for bending are presented in their decoupled form in order to derive an equivalent Timoshenko beam model for the truss. Finally, the physical characteristics of the continuum model are written in terms of the material and geometrical properties of the original truss, which provide a simple tool for comparing dynamic characteristics of lattices with different properties. The natural frequencies are found for each of the bending coordinates of vibration and are compared to those of a standard finite-element method (FEM) solution, for the purpose of validation. The partial differential equations predictions of the natural frequencies for the truss are very close to the FEM. Finally the errors in the frequency estimations are found in terms of the wavelength of the traveling waves.     

Spatial Postbuckling Analysis of Nonsymmetric Thin-Walled Frames.?I: Theoretical Considerations Based on Semitangential Property

To present the spatial postbuckling analysis procedures of shear deformable thin-walled space frames with nonsymmetric cross sections, theoretical considerations based on the semitangential rotation and the semitangential moment are presented. First, similarity and difference between Rodriguez' rotations and semitangential rotations are addressed. Next, the improved displacement field is introduced using the second-order terms of semitangential rotations and rotational properties of off-axis loads and conservative moments are discussed based on the proposed displacement field. Finally, it is deduced that the resulting potential energy due to stress resultants corresponds to semitangential bending and torsional moments. In a companion paper, the elastic strain energy including bending-torsion coupled terms and shear deformation effects is newly derived and a clearly consistent finite-element procedure is presented based on the updated Lagrangian corotational formulation. Tangent stiffness matrices of the thin-walled space frame element are derived using Hermitian polynomials considering shear deformation effects, and a new scheme to evaluate incremental member forces and load correction stiffness matrices due to off-axis loads is presented and its physical meaning is addressed. Furthermore, finite-element solutions displaying spatial postbuckling behaviors are evaluated and compared with available solutions.     

Prediction of Creep Stiffness of Asphalt Mixture with Micromechanical Finite-Element and Discrete-Element Models

This study presents micromechanical finite-element (FE) and discrete-element (DE) models for the prediction of viscoelastic creep stiffness of asphalt mixture. Asphalt mixture is composed of graded aggregates bound with mastic (asphalt mixed with fines and fine aggregates) and air voids. The two-dimensional (2D) microstructure of asphalt mixture was obtained by optically scanning the smoothly sawn surface of superpave gyratory compacted asphalt mixture specimens. For the FE method, the micromechanical model of asphalt mixture uses an equivalent lattice network structure whereby interparticle load transfer is simulated through an effective asphalt mastic zone. The ABAQUS FE model integrates a user material subroutine that combines continuum elements with viscoelastic properties for the effective asphalt mastic and rigid body elements for each aggregate. An incremental FE algorithm was employed in an ABAQUS user material model for the asphalt mastic to predict global viscoelastic behavior of asphalt mixture. In regard to the DE model, the outlines of aggregates were converted into polygons based on a 2D scanned mixture microstructure. The polygons were then mapped onto a sheet of uniformly sized disks, and the intrinsic and interface properties of the aggregates and mastic were assigned for the simulation. An experimental program was developed to measure the properties of sand mastic for simulation inputs. The laboratory measurements of the mixture creep stiffness were compared with FE and DE model predictions over a reduced time. The results indicated both methods were applicable for mixture creep stiffness prediction.     

Multi-level simulation of metal-forming processes

The IBF has for some years made use of finite element programmes to solve metal-forming problems. In the course of this investigation, it has become evident that a problem-oriented adaptation of FEM simulation to the problem in hand is beneficial in terms of computation effort. The computation time for the process parameters is optimised in a multi-level simulation. At level 1 (global analysis) integral parameters such as the required force and required work are computed using a coarse FEM mesh. At level 2 (local analysis) an optimised number of elements is used to determine continuum mechanics parameters like stress, strain and temperature. Microscopic phenomena are simulated at level 3 (microscopic analysis), using special micro-material elements and thermodynamic models.     

Methodology for Impact Modeling of Triaxial Braided Composites Using Shell Elements

In this paper, a two-dimensional triaxial braided composite model has been studied using the nonlinear explicit finite-element code LSDYNA. The unit cell consists of six subcells and material properties associated with shell element integration point simulate braiding architecture. The local material properties were selected by correlation of the global behavior of a coupon model with static specimen tests. By changing subcell size and orientation angle at integration points, different braids architectures were obtained. Panel ballistic models were performed with benefits of computation efficiency of shell elements. Mechanical properties, panel impact threshold velocities, and failure initiations for braids with bias angles of 75, 60, 45, and 30° were studied. Boundary effects were also investigated.     

Spatial Postbuckling Analysis of Nonsymmetric Thin-Walled Frames.?II: Geometrically Nonlinear FE Procedures

In a companion paper, transformation rules of Rodriguez' finite rotations and semitangential rotations are derived, respectively, and their rotational properties are discussed. The shear deformable displacement field of nonsymmetric thin-walled space frames is introduced based on semitangential rotations and the potential energy corresponding to semitangential internal moments are consistently derived using the proposed displacement field. In this paper, for spatial postbuckling analysis of thin-walled space frames, the elastic strain energy including bending-torsion coupled terms and shear deformation effects is derived using transformations of displacements and stress resultants defined at the centroid and the centroid-shear center, respectively. Tangent stiffness matrices of the frame element are derived by using Hermitian polynomials including shear effects, and an improved corotational formulation is presented by separating rigid body motions and pure deformations from incremental displacements, calculating the corresponding generalized forces and updating direction cosines of frame elements. In addition, a scheme to evaluate load correction stiffness matrices due to the off-axis loading and conservative moments is addressed. FE solutions for the postbuckling are presented and compared with results by ABAQUS shell models.     

Numerical Simulations of Upsetting Process of the Fresh Fiber-Cement Paste

In this paper, first, the technical aspects for applications of finite-element method (FEM) in modeling material forming processes are reviewed, with a final determination of employing the solid formulation explicit finite element code, ANSYS/LS-DYNA, with the arbitrary Lagrangian–Eulerian mesh to simulate upsetting process, which is the uniaxial compression of a cylindrical specimen between two flat platens, of the fresh fiber-cement paste. After combining a previously proposed elasto-viscoplastic constitutive model for the fresh fiber-cement paste into the numerical procedure, satisfactory agreement between experimental and simulated results is observed for the upsetting force-imposed displacement data. The evolution of the deformation within the material flow in the upsetting process is then interpreted based on the calculated results. The study indicates that the present finite-element procedure, as well as the material constitutive model and the boundary condition treatment, are appropriate for modeling the upsetting process of the fresh fiber-cement paste.     

Partitioning of Tall Buildings Using Bubble Graph Representation

In this paper it is shown that the current methods of graph representation used for finite-element mesh partitioning are inappropriate for tall buildings, where the mesh will generally consist of both one and two dimensional elements. A new graph representation, called the bubble graph, is proposed and the results of decomposing these graphs using standard graph partitioning tools are presented. The new graph representation is shown to be appropriate for the partitioning of finite-element meshes of tall buildings.     

Solver and Shell Element Performances for Curved Bridge Analysis

A study has been undertaken to investigate different solver and shell element performances for curved bridge finite-element analysis. Three sparse solvers were implemented into a bridge finite-element analysis code, and the solution times and memory requirements for typical bridges were compared. In addition, the use of four-node and nine-node shell elements in modeling was investigated for different mesh densities. Based on the comparative studies performed, modeling guidelines for practicing engineers have been developed and are presented herein.     

Numerical Method for Lower-Bound Solution of the Rigid-Plastic Limit Analysis Problem

This paper describes a numerical method to determine the lower-bound solution of limit load of a rigid–perfectly plastic body obeying the von Mises yield criterion. The idea of this method is to construct a smoothed linear stress field that satisfies the yield criterion everywhere in the body. Applying the similar stress recovery techniques as superconvergent patch recovery and recovery by equilibrium in patch in the elastic finite-element analysis, the nodal stresses are obtained from those stresses at the integration points from an iterative process of upper-bound limit analysis. Then, the improved stress fields and lower-bound solutions can be derived by ensuring all the nodal stresses within the yield surface. The convergence of this method is guaranteed. The validity of the proposed method is demonstrated with some numerical examples. The computational results show that more reliable lower-bound solutions can be obtained by using this method, especially for problems with strain singularity.     

Unified DSC Constitutive Model for Pavement Materials with Numerical Implementation

Need for unified and mechanistic constitutive models for pavement materials for evaluation of various distresses has been recognized; however, such models are not yet available. There have been efforts to develop unified models; however, they have been based usually on ad hoc combinations of models for special properties such as elastic, plastic, creep and fracture, often without appropriate connections to various coupled responses of bound and unbound materials, they may result and in a large number of parameters, often without physical meanings. The disturbed state concept (DSC) provides a modeling approach that includes various responses such as elastic, plastic, creep, microcracking and fracture, softening and healing under mechanical and environmental (thermal, moisture, etc.) within a single unified and coupled framework. A brief review is presented to identify the advantages of the DSC compared to other available models. The DSC has been validated and applied to a wide range of materials: geologic, asphalt, concrete, ceramic, metal alloys, and silicon. It allows for evaluation of various distresses such as permanent deformations (rutting), microcracking and fracture, reflection cracking, thermal cracking, and healing. The DSC is implemented in two- and three-dimensional finite-element (FE) procedures, which allow static, repetitive, and dynamic loads including elastic, plastic, creep, microcracking leading to fracture and failure. A number of examples are solved for various distresses considering flexible (asphalt) pavements; however, the DSC model is applicable to rigid (concrete) pavements also. It is felt that the DSC and the FE computer programs provide unique and novel approaches for pavement engineering. It is desirable to perform further research and applications including validation with respect to simulated and field behavior of pavements.