Michael H. Scott

Nonlinear Finite-Element Analysis Software Architecture Using Object Composition

Object composition offers significant advantages over class inheritance to develop a flexible software architecture for finite-element analysis. Using this approach, separate classes encapsulate fundamental finite-element algorithms and interoperate to form and solve the governing nonlinear equations. Communication between objects in the analysis composition is established using software design patterns. Root-finding algorithms, time integration methods, constraint handlers, linear equation solvers, and degree of freedom numberers are implemented as interchangeable components using the Strategy pattern. The Bridge and Factory Method patterns allow objects of the finite-element model to vary independently from objects that implement the numerical solution procedures. The Adapter and Iterator patterns permit equations to be assembled entirely through abstract interfaces that do not expose either the storage of objects in the analysis model or the computational details of the time integration method. Sequence diagrams document the interoperability of the analysis classes for solving nonlinear finite-element equations, demonstrating that object composition with design patterns provides a general approach to developing and refactoring nonlinear finite-element software.

Dominant-Negative Inhibition of Prion Formation Diminished by Deletion Mutagenesis of the Prion Protein

ABSTRACT Polymorphic basic residues near the C terminus of the prion protein (PrP) in humans and sheep appear to protect against prion disease. In heterozygotes, inhibition of prion formation appears to be dominant negative and has been simulated in cultured cells persistently infected with scrapie prions. The results of nuclear magnetic resonance and mutagenesis studies indicate that specific substitutions at the C-terminal residues 167, 171, 214, and 218 of PrPC act as dominant-negative, inhibitors of PrPSc formation (K. Kaneko et al., Proc. Natl. Acad. Sci. USA 94:10069–10074, 1997). Trafficking of substituted PrPC to caveaola-like domains or rafts by the glycolipid anchor was required for the dominant-negative phenotype; interestingly, amino acid replacements at multiple sites were less effective than single-residue substitutions. To elucidate which domains of PrPC are responsible for dominant-negative inhibition of PrPSc formation, we analyzed whether N-terminally truncated PrP(Q218K) molecules exhibited dominant-negative effects in the conversion of full-length PrPC to PrPSc. We found that the C-terminal domain of PrP is not sufficient to impede the conversion of the full-length PrPC molecule and that N-terminally truncated molecules (with residues 23 to 88 and 23 to 120 deleted) have reduced dominant-negative activity. Whether the N-terminal region of PrP acts by stabilizing the C-terminal domain of the molecule or by modulating the binding of PrPC to an auxiliary molecule that participates in PrPSc formation remains to be established.

A Protease-Resistant 61-Residue Prion Peptide Causes Neurodegeneration in Transgenic Mice

ABSTRACT An abridged prion protein (PrP) molecule of 106 amino acids, designated PrP106, is capable of forming infectious miniprions in transgenic mice (S. Supattapone, P. Bosque, T. Muramoto, H. Wille, C. Aagaard, D. Peretz, H.-O. B. Nguyen, C. Heinrich, M. Torchia, J. Safar, F. E. Cohen, S. J. DeArmond, S. B. Prusiner, and M. Scott, Cell 96:869–878, 1999). We removed additional sequences from PrP106 and identified a 61-residue peptide, designated PrP61, that spontaneously adopted a protease-resistant conformation in neuroblastoma cells. Synthetic PrP61 bearing a carboxy-terminal lipid moiety polymerized into protease-resistant, β-sheet-enriched amyloid fibrils at a physiological salt concentration. Transgenic mice expressing low levels of PrP61 died spontaneously with ataxia. Neuropathological examination revealed accumulation of protease-resistant PrP61 within neuronal dendrites and cell bodies, apparently causing apoptosis. PrP61 may be a useful model for deciphering the mechanism by which PrP molecules acquire protease resistance and become neurotoxic.

Krylov Subspace Accelerated Newton Algorithm: Application to Dynamic Progressive Collapse Simulation of Frames

An accelerated Newton algorithm based on Krylov subspaces is applied to solving nonlinear equations of structural equilib- rium. The algorithm uses a low-rank least-squares analysis to advance the search for equilibrium at the degrees of freedom DOFs where the largest changes in structural state occur; then it corrects for smaller changes at the remaining DOFs using a modified Newton computation. The algorithm is suited to simulating the dynamic progressive collapse analysis of frames where yielding and local collapse mechanisms form at a small number of DOFs while the state of the remaining structural components is relatively linear. In addition, the algorithm is able to resolve erroneous search directions that arise from approximation errors in the tangent stiffness matrix. Numerical examples indicate that the Krylov subspace algorithm has a larger radius of convergence and requires fewer matrix factorizations than Newton-Raphson in the dynamic progressive collapse simulation of reinforced concrete and steel frames. DOI: 10.1061/ASCEST.1943-541X.0000143 CE Database subject headings: Algorithms; Failures; Nonlinear analysis; Progressive collapse; Steel frames. Author keywords: Algorithms; Collapse; Nonlinear analysis; Progressive failure.

Moment-Rotation Behavior of Force-Based Plastic Hinge Elements

The moment-rotation behavior of force-based frame elements is expressed as a function of plastic hinge length and moment-curvature parameters for two types of plastic hinge integration under the representative loading condition of antisymmetric bending. For modified Gauss-Radau hinge integration, there is a unique relationship between the resulting moment-rotation hardening ratio and parameters defining the plastic hinge length and moment-curvature hardening ratio. For two-point Gauss-Radau hinge integration, the spread of yielding across the hinge regions leads to a multilinear moment-rotation response, for which a secant approximation of the hardening stiffness is directed to a target plastic rotation. An example application demonstrates that significantly unconservative assessments of lateral load-carrying capacity can be attained if modeling parameters for plastic hinge length and moment-curvature strain hardening are not calibrated to account for the discrepancy between moment-curvature and moment-rotation behavior of an element.

Affinity-tagged miniprion derivatives spontaneously adopt protease-resistant conformations.

ABSTRACT An abridged PrP molecule of 106 amino acids designated PrP106 can form infectious miniprions in transgenic (Tg) mice (29). Addition of six-histidine (His6) affinity tags to selective sites within PrP106 resulted unexpectedly in new PrP proteins that spontaneously adopted protease-resistant conformations when expressed in neuroblastoma cells and Tg mice. Acquisition of protease resistance depended on the length, charge, and placement of the affinity tag. Introduction of the disease-linked mutation E200K into the sequence of PrP106(140/6His) increased the recovery of protease-resistant PrP fivefold, whereas introduction of the mutations C213A and Δ214–220 did not affect the recovery of protease-resistant PrP. Treatment of cultured cells expressing affinity-tagged PrP106 mutants with polypropyleneimine dendrimer rendered these proteins sensitive to protease digestion in a manner similar to wild-type PrPSc. We conclude that certain affinity-tagged PrP106 proteins spontaneously fold into conformations partially resembling, yet distinct from, wild-type PrPSc. These proteins might be useful tools in the identification of new disease-causing mutations as well as for screening compounds for therapeutic efficacy.

Deterioration modeling of steel moment resisting frames using finite-length plastic hinge force-based beam-column elements

AbstractThe use of empirically calibrated moment-rotation models that account for strength and stiffness deterioration of steel frame members is paramount in evaluating the performance of steel structures prone to collapse under seismic loading. These deterioration models are typically used as zero-length springs in a concentrated plasticity formulation; however, a calibration procedure is required when they are used to represent the moment-curvature (M−χ) behavior in distributed plasticity formulations because the resulting moment-rotation (M−θ) response depends on the element integration method. A plastic hinge integration method for using deterioration models in force-based elements is developed and validated using flexural stiffness modifications parameters to recover the exact solution for linear problems while ensuring objective softening response. To guarantee accurate results in both the linear and nonlinear range of response, the flexural stiffness modification parameters are computed at the begi...

Direct Differentiation of the Particle Finite-Element Method for Fluid–Structure Interaction

AbstractSensitivity analysis of fluid–structure interaction (FSI) provides an important tool for assessing the reliability and performance of coastal infrastructure subjected to storm and tsunami hazards. As a preliminary step for gradient-based applications in reliability, optimization, system identification, and performance-based engineering of coastal infrastructure, the direct differentiation method (DDM) is applied to FSI simulations using the particle finite-element method (PFEM). The DDM computes derivatives of FSI response with respect to uncertain design and modeling parameters of the structural and fluid domains that are solved in a monolithic system via the PFEM. Geometric nonlinearity of the free surface fluid flow is considered in the governing equations of the DDM along with sensitivity of material and geometric nonlinear response in the structural domain. The analytical derivatives of elemental matrices and vectors with respect to element properties are evaluated and implemented in an open ...

Deciphering Prion Diseases with Transgenic Mice

Prions cause a group of human and animal neurodegenerative diseases that are now classified together because their etiology and pathogenesis involve modification of the prion protein (PrP) (1). Prion diseases are manifest as infectious, genetic, and sporadic disorders (Table 16.1). These diseases can be transmitted among mammals by the infectious particle designated “prion” (2). Despite intensive searches over the past three decades, no nucleic acid has been found within prions (3–6), yet a modified isoform of the host-encoded PrP designated PrPSc is essential for infectivity (1, 7–10). In fact, considerable experimental data argue that prions are composed exclusively of PrPSc. Earlier terms used to describe the prion diseases include transmissible encephalopathies, spongiform encephalopathies, and slow virus diseases (11–13).

Evaluation of Force-Based Frame Element Response Sensitivity Formulations

The direct differentiation method (DDM) has been shown to be an accurate and efficient approach to computing the sensitivity of structural response to uncertain parameters of constitutive models and finite-element formulations. Although it is well-known that the DDM should be consistent with the numerical time stepping procedure at the structural level, it is possible for element-level numerical instabilities to arise when the response sensitivity equations are inconsistent with the equations that govern the element response. Two existing formu- lations of DDM force-based element response sensitivity are shown to be mathematically equivalent in exact arithmetic; however, only one is consistent with the force-based response equations and possesses a low condition number for finite arithmetic. On the other hand, the in- consistent formulation has a high condition number that is equal to the product of the largest singular values of the section and element stiffness matrices. Representative examples show that the high condition number of the inconsistent formulation is innocuous for sensitivity with respect to section-level parameters but can lead to round off errors for sensitivity with respect to element-level geometric parameters. DOI: 10.1061/(ASCE)ST.1943-541X.0000447.