scholarly journals From Stress to Shape: Equilibrium of Cloister and Cross Vaults

2021 ◽  
Vol 11 (9) ◽  
pp. 3846
Author(s):  
Andrea Montanino ◽  
Carlo Olivieri ◽  
Giulio Zuccaro ◽  
Maurizio Angelillo
Keyword(s):  
Error Function ◽  
Membrane Surface ◽  
Equilibrium Analysis ◽  
Test Cases ◽  
Order Partial Differential Equation ◽  
Negative Semidefinite ◽  
Historical Heritage ◽  
Masonry Vaults ◽  
Membrane Shape ◽  
The Given

The assessment of the equilibrium and the safety of masonry vaults is of high relevance for the conservation and restoration of historical heritage. In the literature many approaches have been proposed for this tasks, starting from the 17th century. In this work we focus on the Membrane Equilibrium Analysis, developed under the Heyman’s theory of Limit Analysis. Within this theory, the equilibrium of a vault is assessed if it is possible to find at least one membrane surface, between the volume of the vaults, being in equilibrium under the given loads through a purely compressive stress field. The equilibrium of membranes is described by a second order partial differential equation, which is definitely elliptic only when a negative semidefinite stress is assigned, and the shape is the unknown of the problem. The proposed algorithm aims at finding membrane shapes, entirely comprised between the geometry of the vault, in equilibrium with admissible stress fields, through the minimization of an error function with respect to shape parameters of the stress potential, and then, with respect to the boundary values of the membrane shape. The application to two test cases shows the viability of this tool for the assessment of the equilibrium of existing masonry vaults.

An Inverse Inviscid Method for the Design of Quasi-Three-Dimensional Turbomachinery Cascades

1993 ◽  
Vol 115 (1) ◽  
pp. 121-127 ◽  
Author(s):  
E. Bonataki ◽  
P. Chaviaropoulos ◽  
K. D. Papailiou
Keyword(s):  
Differential Equation ◽  
Three Dimensional ◽  
Test Cases ◽  
Elliptic Type ◽  
Flow Angle ◽  
Blade Shape ◽  
Closure Conditions ◽  
Type Boundary ◽  
Absolute Frame ◽  
The Given

The calculation of the blade shape, when the desired velocity distribution is imposed, has been the object of numerous investigations in the past. The object of this paper is to present a new method suitable for the design of turbomachinery stator and rotor blade sections, lying on an arbitrary axisymmetric stream-surface with varying streamtube width. The flow is considered irrotational in the absolute frame of reference and compressible. The given data are the streamtube geometry, the number of blades, the inlet flow conditions and the suction and pressure side velocity distributions as functions of the normalized arc-length. The output of the computation is the blade shape that satisfies the above data. The method solves an elliptic type partial differential equation for the velocity modulus with Dirichlet and periodic type boundary conditions on the (potential function, stream function)-plane (Φ, Ψ). The flow angle field is subsequently calculated solving an ordinary differential equation along the iso-Φ or iso-Ψ lines. The blade coordinates are, finally, computed by numerical integration. A set of closure conditions has been developed and discussed in the paper. The method is validated on several test cases and a discussion is held concerning its application and limitations.

scholarly journals Numerical Solution for the Extrapolation Problem of Analytic Functions

Research ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Nikolaos P. Bakas
Keyword(s):  
Numerical Solution ◽  
Basis Functions ◽  
Test Cases ◽  
Multiple Dimensions ◽  
Error Magnitude ◽  
Approximation Errors ◽  
Rapid Calculation ◽  
Extrapolation Problem ◽  
The Given ◽  
Domain Length

In this work, a numerical solution for the extrapolation problem of a discrete set of n values of an unknown analytic function is developed. The proposed method is based on a novel numerical scheme for the rapid calculation of higher order derivatives, exhibiting high accuracy, with error magnitude of O(10−100) or less. A variety of integrated radial basis functions are utilized for the solution, as well as variable precision arithmetic for the calculations. Multiple alterations in the function’s direction, with no curvature or periodicity information specified, are efficiently foreseen. Interestingly, the proposed procedure can be extended in multiple dimensions. The attained extrapolation spans are greater than two times the given domain length. The significance of the approximation errors is comprehensively analyzed and reported, for 5832 test cases.

scholarly journals Selected problems of failures and repairs of historic masonry vaults

2019 ◽  
Vol 284 ◽  
pp. 05008 ◽  
Author(s):  
Rafał Nowak ◽  
Romuald Orłowicz
Keyword(s):  
Model Calibration ◽  
Technical Condition ◽  
Critical Conditions ◽  
Heritage Preservation ◽  
In Situ Tests ◽  
Historic Masonry ◽  
Historical Heritage ◽  
Masonry Vaults ◽  
Condition State

The paper discusses the technical condition (state) of existing vaults. Several examples of critical conditions of vaults are presented. Analysis and proper modelling of vaults is discussed. Repair methods were proposed with respect to historical heritage preservation. The maintenance methods of vaults were discussed with pointing the crucial elements. It was noticed that in situ tests are necessary for proper model calibration and repair results verification.

scholarly journals Cutting Path Optimization Using Tabu Search

2011 ◽  
Vol 473 ◽  
pp. 739-748 ◽  
Author(s):  
Reginald Dewil ◽  
Pieter Vansteenwegen ◽  
Dirk Cattrysse
Keyword(s):  
Tabu Search ◽  
Software Package ◽  
Feasible Solution ◽  
Test Cases ◽  
Finish Cutting ◽  
Initial Feasible Solution ◽  
Commercial Software Package ◽  
Cutter Head ◽  
Cutting Path ◽  
The Given

This paper deals with generating paths for cutting irregular parts nested on a metal sheet. The objective is to minimize the total non-cutting time for the cutter head starting at a known location, cutting all the required elements and returning to the known location. In contrast to most literature on this topic, a part does not have to be cut at once. If this reduces the total non-cutting time, it is possible to cut a number of elements on a given part, then cut other parts and then return later to finish cutting the given part. The problem is modeled as a generalized traveling salesperson problem with special precedence constraints. An initial feasible solution is generated and improved by local moves embedded in a tabu search framework. The proposed algorithm shows promising results in comparison with a commercial software package on a limited set of test cases.

scholarly journals Numerical Simulation for the Treatment of Nonlinear Predator–Prey Equations by Using the Finite Element Optimization Method

2021 ◽  
Vol 5 (2) ◽  
pp. 56
Author(s):  
H. M. Srivastava ◽  
M. M. Khader
Keyword(s):  
Finite Element ◽  
Error Function ◽  
Optimization Method ◽  
Algebraic Equations ◽  
The Finite Element Method ◽  
Predator Prey ◽  
Efficient Simulation ◽  
Runge Kutta Method ◽  
Proposed Model ◽  
The Given

This article aims to introduce an efficient simulation to obtain the solution for a dynamical–biological system, which is called the Lotka–Volterra system, involving predator–prey equations. The finite element method (FEM) is employed to solve this problem. This technique is based mainly upon the appropriate conversion of the proposed model to a system of algebraic equations. The resulting system is then constructed as a constrained optimization problem and optimized in order to get the unknown coefficients and, consequently, the solution itself. We call this combination of the two well-known methods the finite element optimization method (FEOM). We compare the obtained results with the solutions obtained by using the fourth-order Runge–Kutta method (RK4 method). The residual error function is evaluated, which supports the efficiency and the accuracy of the presented procedure. From the given results, we can say that the presented procedure provides an easy and efficient tool to investigate the solution for such models as those investigated in this paper.

scholarly journals Concurrency testing using symbolic path finder

2018 ◽  
Vol 7 (2.6) ◽  
pp. 275
Author(s):  
Bidush Kumar Sahoo ◽  
Mitrabinda Ray
Keyword(s):  
Symbolic Execution ◽  
Concurrent Programs ◽  
Test Case ◽  
Test Cases ◽  
Concurrent Program ◽  
Activity Complex ◽  
Race Condition ◽  
Concurrent Testing ◽  
Concurrency Testing ◽  
The Given

Concurrent programs have specific features such as italic communication, synchronization and nondeterministic behavior that make the testing activity complex. The objective is to find various types of concurrent defects. In this paper, we have used a model checking tool called Symbolic Path Finder (SPF) which is the upgradation of Java Path Finder (JPF) for concurrent testing. SPF is used for generating the test cases to check concurrent defects such as deadlock, race condition etc. SPF generates symbolic execution tree of the given code which is used as an input for test case generation. The execution is done for finding the test cases in concurrent program where number of threads is operating together with the concurrent defects. The test cases show the type of concurrent defects in the respective line number of the source code.  

scholarly journals Report of the IAU WGAS Sub-group on Standard Procedures

1995 ◽  
Vol 10 ◽  
pp. 185-189 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Computational Procedure ◽  
Test Cases ◽  
The Third ◽  
Standard Procedures ◽  
Readable Form ◽  
Fundamental Astronomy ◽  
Written Form ◽  
Machine Readable ◽  
The Given ◽  
Machine Readable Form

The given mission of the subgroup on Standard Procedures (SGSP) of IAUWGon Astronomical Standards (IAU/WGAS) is to prepare report “on standard procedures needed in fundamental astronomy, which a) should have a maximum degree of compatibility with the IERS Standards, b) should include the implementations of procedures in the form of tested software and/or test cases, c) should be available not only in written form, but also in machine-readable form” as described in the third item of Recommendation VIII of the IAU Resolution A4 (1991). After some general discussions, in 1992 we issued a questionnaire on the image and mechanism on the supposed set of standard procedures (IAU/WGAS Circulrar 51.2.1) and sent it to over 200 scientists in the world. Within a few months, 16 answers were sent back. The detailed answers and the questionnaire was distributed (IAU/WGAS Circular 54.2.1). As a simulation of supposed mechanism, in 1993 we did a test campaign to collect computational procedure(s) to compute the present IAU precession formula (Lieske et al., 1979) in FORTRAN (IAU/WGAS Circular 59.2.1). Within a few months, 5 submissions from 5 countires (Japan, China, USA, Russia, and UK) reached. The analysis of submitted routines was circulated (IAU/WGAS Circular 65.2.1). Based on these responses, we concluded that the establishment of a mechanism to provide such procedures to the community of astronomy is quite useful. To realize this, we will recommend some action items to the IAU as is described in the next Section. Its main purpose is to establish a mechanism by the combination of a comiittee of board and a center, which are to operate within a year after the recommendations are adopted by the IAU. Section 3 will describe some guidelines for the committee and center to perform the tasks to create and maintain standard procedures. Of course, these are to be consulted if necessary and are not to restrict or regulate the activity of the committee and the center.

scholarly journals An Accurate Approximation of the Two-Phase Stefan Problem with Coefficient Smoothing

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1924
Author(s):  
Vasily Vasil’ev ◽  
Maria Vasilyeva
Keyword(s):  
Phase Change ◽  
Stefan Problem ◽  
Error Function ◽  
Discontinuous Coefficients ◽  
Two Phase ◽  
Spatial Interval ◽  
The One ◽  
Transfer Problems ◽  
The Mathematical Model ◽  
The Given

In this work, we consider the heat transfer problems with phase change. The mathematical model is described through a two-phase Stefan problem and defined in the whole domain that contains frozen and thawed subdomains. For the numerical solution of the problem, we present three schemes based on different smoothing of the sharp phase change interface. We propose the method using smooth coefficient approximation based on the analytical smoothing of discontinuous coefficients through an error function with a given smoothing interval. The second method is based on smoothing in one spatial interval (cell) and provides a minimal length of smoothing calculated automatically for the given values of temperatures on the mesh. The third scheme is a convenient scheme using a linear approximation of the coefficient on the smoothing interval. The results of the numerical computations on a model problem with an exact solution are presented for the one-dimensional formulation. The extension of the method is presented for the solution of the two-dimensional problem with numerical results.

Coverage Criteria for State-Based Testing

2019 ◽  
Vol 10 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Sonali Pradhan ◽  
Mitrabinda Ray ◽  
Srikanta Patnaik
Keyword(s):  
Dynamic Behaviour ◽  
Mutation Testing ◽  
Test Cases ◽  
State Machines ◽  
Round Trip ◽  
Coverage Criteria ◽  
State Chart ◽  
Path Testing ◽  
The Given ◽  
Intermediate Graph

State-based testing (SBT) is known as deriving test cases from state machines and examining the dynamic behaviour of the system. It helps to identify various types of state-based faults within a system under test (SUT). For SBT, test cases are generated from state chart diagrams based on various coverage criteria such as All Transition, Round Trip Path, All Transition Pair, All Transition Pair with length 2, All Transition Pair with length 3, All Transition Pair of length 4 and Full Predicate. This article discuses a number of coverage criteria at the design level to find out various types of state-based faults in SBT. First, the intermediate graph is generated from a state chart diagram using an XML parser. The graph is traversed based on the given coverage criteria to generate a sequence of test cases. Then, mutation testing and sneak-path testing are applied on the generated test cases to check the effectiveness of the generated test suite. These two are common methods for checking the effectiveness of test cases. Mutation testing helps in the number of seeded errors covered whereas sneak-path testing basically helps to examine the unspecified behavior of the system. In round trip path (RTP), it is not possible to cover all paths. All transition is not an adequate level of fault detection with more execution time compared to all transition pair (ATP) with length 4 (LN4). In the discussion, ATP with LN4 is the best among all coverage criteria. SBT can able to detect various state-based faults-incorrect transition, missing transition, missing or incorrect event, missing or incorrect action, extra missing or corrupt state, which are difficult to detect in code-based testing. Most of these state-based faults can be avoided, if the testing is conducted at the early phase of design.

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