Summary
We present a computational framework for the simulation of J2‐elastic/plastic materials in complex geometries based on simple piecewise linear finite elements on tetrahedral grids. We avoid ...spurious numerical instabilities by means of a specific stabilization method of the variational multiscale kind. Specifically, we introduce the concept of subgrid‐scale displacements, velocities, and pressures, approximated as functions of the governing equation residuals. The subgrid‐scale displacements/velocities are scaled using an effective (tangent) elastoplastic shear modulus, and we demonstrate the beneficial effects of introducing a subgrid‐scale pressure in the plastic regime. We provide proofs of stability and convergence of the proposed algorithms. These methods are initially presented in the context of static computations and then extended to the case of dynamics, where we demonstrate that, in general, naïve extensions of stabilized methods developed initially for static computations seem not effective. We conclude by proposing a dynamic version of the stabilizing mechanisms, which obviates this problematic issue. In its final form, the proposed approach is simple and efficient, as it requires only minimal additional computational and storage cost with respect to a standard finite element relying on a piecewise linear approximation of the displacement field.
The results of experimental tests and finite element (FE) simulations are used to develop a stiffness model that predicts the behavior of bolted thick built-up T-stub connections including column ...flange deformation, and accounting for primary and secondary prying effect. The model incorporates the overall T-stub and column flange deformations of key component elements, and includes nonlinear material behavior of bolts and base material, and accounts for pretension of fasteners and contact interactions. The stiffness model consists of linear and nonlinear springs which model deformations from tension bolt elongation, slip-bearing, bending of T-stub flange, elongation of the T-stem, column flange deformation, and accounts for primary and secondary prying forces. The behavioral characteristics of the T-stub/column flange system are examined including strength, stiffness, deformation, and energy dissipation. A proposed strength model that predicts the capacity of the column flange for the failure mode of full plastification at the flange-to-web connection of the column (K-zone) followed by interior tension bolt fracture is developed. Furthermore, closed form expressions that are based on stiffness modeling techniques are developed to predict the energy dissipation capacity of the T-stub/column flange system with and without continuity plates. Comparison of the models predictions with experimental and FE data shows that the proposed models accurately predict the connection and the column flange load-deformation response. This study provides guidelines for engineers to account for the additional forces induced in the tension bolts and for the maximum rotational capacity demand in the connection which are required for seismic analysis and design.
•Stiffness-based model predicts the force-deformation of T-stub/column flange.•The model takes into account the effect of secondary prying.•Strength model for K-zone plastification followed by interior tension bolt fracture.•New failure limit states are highlighted.•Simple tool in predicting strength, stiffness, ductility, and energy dissipation.
Double angle connections are one of the common simple beam-end framing connections used in steel structures, but current building standards do not provide much guidance on how to design these ...connections for fire. Development of such design methodologies is particularly hindered by the lack of adequate understanding of the strength and deformation capacities of double angle connections in fire. To address this issue, this paper presents key results of a computational study of the influence of fire temperatures on steel double angle connections. Computational models for double angle connections are developed in Abaqus and evaluated against experimental data from the literature at both ambient and elevated temperatures. An extensive study is then conducted to investigate different parameters that impact the behavior of double angle connection assemblies during a fire. A comparison is also made between the performances of double angle and shear tab connections at elevated temperatures. Results obtained in this study show that the main factors impacting the behavior of double angle connections at elevated temperatures are load ratio, initial cooling temperature, location of the double angle with respect to the beam neutral axis, and the gap distance. In addition, double angle connections showed better performance at elevated temperatures when compared to shear tab connections.
•Influence of fire temperatures on steel double angle connections are investigated.•FE models are developed and validated against experimental data in literature.•Important parameters are evaluated.•Comparison with shear tab connections is made.
•A new algorithm for multiplicative nonlinear deviatoric viscoelasticity.•Stable computations on piecewise linear finite elements on triangular and tetrahedral grids.•Nearly and fully incompressible ...materials.•Variational multiscale stabilization scaled with the viscous energy dissipation.
We present a computational approach to solve problems in multiplicative nonlinear viscoelasticity using piecewise linear finite elements on triangular and tetrahedral grids, which are very versatile for simulations in complex geometry. Our strategy is based on (1) formulating the equations of mechanics as a mixed first-order system, in which a rate form of the pressure equation is utilized in place of the standard constitutive relationship, and (2) utilizing the variational multiscale approach, in which the stabilization parameter is scaled with the viscous energy dissipation.
The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate ...(approximate) computational domain. The surrogate domain is constructed so as to avoid cut cells and the associated problematic implementation and numerical integration issues. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions: hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we extend the SBM to the simulation of incompressible Stokes flow, by appropriately weighting its variational form with the elemental volume fraction of active fluid. This approach allows to drastically reduce spurious pressure oscillations in time, which are produced if the total volume of active fluid were to change abruptly over a time step. The proposed Weighted SBM (W-SBM) exactly preserves states of hydrostatic equilibrium, and induces small mass and momentum conservation errors, which converge as the grid is refined. This is in analogy to cutFEMs and related unfitted approaches, which rely on an affine representation of cut boundaries. We demonstrate the robustness and accuracy of the proposed method with an extensive suite of two-dimensional tests.
•The Weighted Shifted Boundary Method (W-SBM) is extended to Stokes flow with moving boundaries.•New no-slip conditions are developed, with optimal accuracy.•Spurious pressure oscillations in time are drastically reduced by volume fraction weighting.•The mass and momentum conservation errors rapidly decay as the mesh are refined.•Extensive numerical testing is performed, including the limit of extremely small time steps.
Summary
In this article, we develop a dynamic version of the variational multiscale (D‐VMS) stabilization for nearly/fully incompressible solid dynamics simulations of viscoelastic materials. The ...constitutive models considered here are based on Prony series expansions, which are rather common in the practice of finite element simulations, especially in industrial/commercial applications. Our method is based on a mixed formulation, in which the momentum equation is complemented by a pressure equation in rate form. The unknown pressure, displacement, and velocity are approximated with piecewise linear, continuous finite element functions. To prevent spurious oscillations, the pressure equation is augmented with a stabilization operator specifically designed for viscoelastic problems, in that it depends on the viscoelastic dissipation. We demonstrate the robustness, stability, and accuracy properties of the proposed method with extensive numerical tests in the case of linear and finite deformations.
We propose a Lagrangian solid mechanics framework for the simulation of salt tectonics and other large‐deformation geomechanics problems at the basin scale. Our approach relies on general ...elastic‐viscoplastic constitutive models to characterize the deformation of geologic strata, in contrast with the majority of published works on the subject, which utilize nonlinear Stokes flow models. By means of multiscale asymptotics, we also show that the inertia term in the momentum balance equation can be safely neglected, if the goal is to track the Earth's crust deformation over long periods of time. Our time integration strategy is a blended transient/quasistatic approach, in that it consists of a constitutive stress update, subject to the constraint that the stresses must satisfy static equilibrium. In addition, we use stabilized finite element methods specifically built for triangular and tetrahedral grids, which can also perform well under incompressibility constraints. Our approach offers computational geologists the following advantages: (1) improved flexibility in the choice of subsurface constitutive models with respect to the nonlinear Stokes flow; (2) improved efficiency over transient dynamics algorithms used in this context in the past, which are forced to resolve seismic events over geologic time scales; and (3) improved robustness in large strain computations over quadrilateral/hexahedral finite elements. We demonstrate the performance of the proposed approach with simulations of passive diapirism.
In this work, a stabilized finite element framework is developed to simulate small and large deformation solid mechanics problems involving complex geometries and complicated constitutive models. In ...particular, the focus is on solid dynamics problems involving nearly and fully incompressible materials. The work is divided into three main themes, the first is concerned with the development of stabilized finite element algorithms for hyperelastic materials, the second handles the case of viscoelastic materials, and the third focuses on algorithms for J2-plastic materials. For all three cases, problems in the small and large deformation regime are considered, and for the J2-plasticity case, both quasi-static and dynamic problems are examined.Some of the key features of the algorithms developed in this work is the simplicity of their implementation into an existing finite element code, and their applicability to problems involving complicated geometries. The former is achieved by using a mixed formulation of the solid mechanics equations where the velocity and pressure unknowns are represented by linear shape functions, whereas the latter is realized by using triangular elements which offer numerous advantages compared to quadrilaterals, when meshing complicated geometries. To achieve the stability of the algorithm, a new approach is proposed in which the variational multiscale approach is applied to the mixed form of the solid mechanics equations written down as a first order system, whereby the pressure equation is cast in rate form.Through a series of numerical simulations, it is shown that the stability properties of the proposed algorithm is invariant to the constitutive model and the time integrator used. By running convergence tests, the algorithm is shown to be second order accurate, in the L2-nrom, for the displacements, velocities, and pressure. Finally, the robustness of the algorithm is showcased by considering realistic test cases involving complicated geometries and very large deformation.
Hypothermic cardiopulmonary bypass with intervals of circulatory arrest is a useful adjunct during operations on the descending thoracic aorta and distal aortic arch when severe aortic disease ...precludes placement of clamps on the aorta. Hypothermia also has a marked protective effect on spinal cord function during periods of aortic occlusion.
Fifty-one patients (age range, 22 to 79 years) with descending thoracic or thoracoabdominal aortic disease had resection and graft replacement of the diseased aortic segments using hypothermic cardiopulmonary bypass and intervals of circulatory arrest in situations where the location, extent, or severity of disease precluded placement of clamps on the proximal aorta (8 patients) or (in 43 patients) when extensive thoracic (11) or thoracoabdominal (32) aortic disease was present and the risk for development of spinal cord ischemic injury and renal failure was judged to be increased. Patent intercostal (below T-6) and upper lumbar arteries were attached to the graft whenever possible.
Thirty-day mortality was 9.8% (5 patients). Paraplegia occurred in 2 and paraparesis in 1 of the 46 30-day survivors (6.5%). Among the 27 operative survivors with thoracoabdominal aneurysms, paraplegia occurred in 1 of 12 with Crawford type I (8%), 0 of 10 with type II, and 1 of 5 with type III aneurysms (20%). Paraplegia occurred in none of the 12 patients with aortic dissection and in 2 of the 15 patients with degenerative aneurysms. Renal failure requiring dialysis occurred in 1 (2.2%) of the 46 30-day survivors.
Hypothermic circulatory arrest is a valuable adjunct for the treatment of complex aortic disease involving the aortic arch and thoracoabdominal aorta. In patients with thoracoabdominal aneurysms, its use has been associated with a low incidence of renal failure and an incidence of paraplegia/paraparesis in traditionally high-risk subsets (type I and II aneurysms, aortic dissection), which may be less than that observed with other surgical techniques.
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