A cell-based smoothed finite element method for kinematic limit analysis

This paper presents a new numerical procedure for kinematic limit analysis problems, which incorporates the cell-based smoothed finite element method with second-order cone programming. The application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort. The non-smooth optimization problem is formulated as a problem of minimizing a sum of Euclidean norms, ensuring that the resulting optimization problem can be solved by an efficient second-order cone programming algorithm. Plane stress and plane strain problems governed by the von Mises criterion are considered, but extensions to problems with other yield criteria having a similar conic quadratic form or 3D problems can be envisaged

LOWER BOUND LIMIT ANALYSIS OF MASONRY PLATES IN TWO- WAY BENDING BY MEANS OF FULL 3D ELEMENTS

The paper provides a novel Lower Bound (LB) Limit Analysis (LA) Finite Element (FE) model for the study at failure of masonry walls in two-way bending by means of full 3D elements. The method of hexahedral discretization is used, while assuming infinite resistance and a quadrilateral interface where all plastic dissipation occurs. It can more accurately analyze the collapse mechanism of masonry panels in the process of two-way bending. It chose two cases to study. They are three series of panels with and without perforations tested at collapse at the University of Adelaide Australia and four series of solid and perforated panels tested at the University of Plymouth UK. The feasibility of the research method was verified. The obtained research results show that the use of the method proposed allows to provide a safe prediction of the existing LA code based on kinematics theorem, with a small computational burden, and the obtained results are more in line with the actual situation and have better practical effects.T The original abstract is titled: 'Out of Plane Lower Bound Limit Analysis&#39

A note on the penalty parameter in Nitsche's method for unfitted boundary value problems

Nitsche's method is a popular approach to implement Dirichlet-type boundary conditions in situations where a strong imposition is either inconvenient or simply not feasible. The method is widely applied in the context of unfitted finite element methods. From the classical (symmetric) Nitsche's method it is well-known that the stabilization parameter in the method has to be chosen sufficiently large to obtain unique solvability of discrete systems. In this short note we discuss an often used strategy to set the stabilization parameter and describe a possible problem that can arise from this. We show that in specific situations error bounds can deteriorate and give examples of computations where Nitsche's method yields large and even diverging discretization errors

Improving Loss Estimation for Woodframe Buildings. Volume 2: Appendices

This report documents Tasks 4.1 and 4.5 of the CUREE-Caltech Woodframe Project. It presents a theoretical and empirical methodology for creating probabilistic relationships between seismic shaking severity and physical damage and loss for buildings in general, and for woodframe buildings in particular. The methodology, called assembly-based vulnerability (ABV), is illustrated for 19 specific woodframe buildings of varying ages, sizes, configuration, quality of construction, and retrofit and redesign conditions. The study employs variations on four basic floorplans, called index buildings. These include a small house and a large house, a townhouse and an apartment building. The resulting seismic vulnerability functions give the probability distribution of repair cost as a function of instrumental ground-motion severity. These vulnerability functions are useful by themselves, and are also transformed to seismic fragility functions compatible with the HAZUS software. The methods and data employed here use well-accepted structural engineering techniques, laboratory test data and computer programs produced by Element 1 of the CUREE-Caltech Woodframe Project, other recently published research, and standard construction cost-estimating methods. While based on such well established principles, this report represents a substantially new contribution to the field of earthquake loss estimation. Its methodology is notable in that it calculates detailed structural response using nonlinear time-history structural analysis as opposed to the simplifying assumptions required by nonlinear pushover methods. It models physical damage at the level of individual building assemblies such as individual windows, segments of wall, etc., for which detailed laboratory testing is available, as opposed to two or three broad component categories that cannot be directly tested. And it explicitly models uncertainty in ground motion, structural response, component damageability, and contractor costs. Consequently, a very detailed, verifiable, probabilistic picture of physical performance and repair cost is produced, capable of informing a variety of decisions regarding seismic retrofit, code development, code enforcement, performance-based design for above-code applications, and insurance practices

GPU-accelerated discontinuous Galerkin methods on hybrid meshes

We present a time-explicit discontinuous Galerkin (DG) solver for the time-domain acoustic wave equation on hybrid meshes containing vertex-mapped hexahedral, wedge, pyramidal and tetrahedral elements. Discretely energy-stable formulations are presented for both Gauss-Legendre and Gauss-Legendre-Lobatto (Spectral Element) nodal bases for the hexahedron. Stable timestep restrictions for hybrid meshes are derived by bounding the spectral radius of the DG operator using order-dependent constants in trace and Markov inequalities. Computational efficiency is achieved under a combination of element-specific kernels (including new quadrature-free operators for the pyramid), multi-rate timestepping, and acceleration using Graphics Processing Units.Comment: Submitted to CMAM

Machine Precision Evaluation of Singular and Nearly Singular Potential Integrals by Use of Gauss Quadrature Formulas for Rational Functions

A new technique for machine precision evaluation of singular and nearly singular potential integrals with 1/R singularities is presented. The numerical quadrature scheme is based on a new rational expression for the integrands, obtained by a cancellation procedure. In particular, by using library routines for Gauss quadrature of rational functions readily available in the literature, this new expression permits the exact numerical integration of singular static potentials associated with polynomial source distributions. The rules to achieve the desired numerical accuracy for singular and nearly singular static and dynamic potential integrals are presented and discussed, and several numerical examples are provide