Search results for: Lefchetz numbers of iterations
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Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs
PublicationGiven a graph G= (V, E), the subdivision of an edge e=uv∈E(G) means the substitution of the edge e by a vertex x and the new edges ux and xv. The domination subdivision number of a graph G is the minimum number of edges of G which must be subdivided (where each edge can be subdivided at most once) in order to increase the domination number. Also, the domination multisubdivision number of G is the minimum number of subdivisions...
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Balancing agility and discipline in a research project
PublicationSuccessful software development requires both agility and discipline. Optimal selection of methods, however, is not an easy task. The problem becomes even more difficult for long lasting projects. Appropriate selection of methods involving skillful introduction and abandonment of certain practices in time makes the whole process dynamic. The paper presents in this context a research project which was realized in a few iterations....
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Numerical simulation of natural convection of Glycol-Al2O3 nanofluids from a horizontal cylinder
PublicationThis paper deals with natural convection around a circular cylinder with constant heat flux in a cavity using computational fluid dynamics. As fluids ethylene glycol and a mixture of ethylene glycol with Al2O3 nanoparticles (mass concentrations of nanoparticles: 0.1% and 1%) are chosen. Rayleigh number ranges from 3104 to 3105. The nanofluids are modeled with single-phase approach. For the investigated range of nanoparticle concentration, the...
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A novel genetic approach to provide differentiated levels of service resilience in IP-MPLS/WDM networks
PublicationThis paper introduces a novel class-based method of survivable routing for connection-oriented IP-MPLS/WDM networks, called MLS-GEN-H. The algorithm is designed to provide differentiated levels of service survivability in order to respond to varying requirements of end-users. It divides the complex problem of survivable routing in IP-MPLS/WDM networks into two subproblems, one for each network layer, which enables finding the...
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Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds
PublicationLet M be a smooth closed simply-connected 4-dimensional manifold, f be a smooth self-map of M with fast grow of Lefschetz numbers and r be a product of different primes. The authors calculate the invariant equal to the minimal number of r-periodic points in the smooth homotopy class of f.
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Mersenne Number Finding and Collatz Hypothesis Verification in the Comcute Grid System
PublicationIn this chapter, some mathematic applications have been described to test scalability of the Comcute grid system. Especially, a verification of the Collatz hypothesis and finding Mersenne numbers were applied to prove the scalability and high performance of this grid system. Results were compared with outcomes obtained by the other grid systems.
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On simplification of residue scaling process in pipelined Radix-4 MQRNS FFT processor
PublicationResidue scaling is needed in pipelined FFT radix-4 processors based on the Modified Quadratic Residue Number System (MQRNS) at the output of each butterfly. Such processor uses serial connection of radix-4 butterflies. Each butterfly comprises n subunits, one for each modulus of the RNS base and generates four complex residue numbers. In order to prevent arithmetic overflow intermediate results after each butterfly have to be...
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Weak forms of shadowing in topological dynamics
PublicationWe consider continuous maps of compact metric spaces. It is proved that every pseudotrajectory with sufficiently small errors contains a subsequence of positive density that is point-wise close to a subsequence of an exact trajectory with the same indices. Also, we study homeomor- phisms such that any pseudotrajectory can be shadowed by a finite number of exact orbits. In terms of numerical methods this property (we call it multishadowing)...
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Fast Full-Wave Multilevel Zero-Pole Optimization of Microwave Filters
PublicationA new concept is proposed for the full-wave computer-aided design of microwave filters. The method consists of two stages and operates on the zeros and poles of the transfer function and their derivatives. These quantities are evaluated from the response computed by a full-wave electromagnetic solver with two levels of accuracy. The two stages make use of different models that are optimized using a low-accuracy electromagnetic...
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On the interspike-intervals of periodically-driven integrate-and-fire models
PublicationWe analyze properties of the firing map, which iterations give information about consecutive spikes, for periodically driven linear integrate-and-fire models. By considering locally integrable (thus in general not continuous) input functions, we generalize some results of other authors. In particular, we prove theorems concerning continuous dependence of the firing map on the input in suitable function spaces. Using mathematical...
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Pareto Ranking Bisection Algorithm for Expedited Multi-Objective Optimization of Antenna Structures
PublicationThe purpose of this letter is introduction of a novel methodology for expedited multi-objective design of antenna structures. The key component of the presented approach is fast identification of the initial representation of the Pareto front (i.e., a set of design representing the best possible trade-offs between conflicting objectives) using a Pareto-ranking bisection algorithm. The algorithm finds a discrete set of Pareto-optimal...
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VARIANT DESIGNING IN the PRELIMINARY SMALL SHIP DESIGN PROCESS
PublicationShip designing is a complex process, as the ship itself is a complex, technical multi-level object which operates in the air/water boundary environment and is exposed to the action of many different external and internal factors resulting from the adopted technical solutions, type of operation, and environmental conditions. A traditional ship design process consists of a series of subsequent multistage iterations, which gradually...
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Criteria for selection of working fluid in low-temperature ORC
PublicationThe economics of an ORC system is strictly linked to thermodynamic properties of the working fluid. A bad choice of working fluid could lead to a less efficient and expensive plant/generation unit. Some selection criteria have been put forward by various authors, incorporating thermodynamic properties, provided in literature but these do not have a general character. In the paper a simple analysis has been carried out which resulted...
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Stark effect of atomic helium singlet lines
PublicationWe present experimental and theoretical investigations of the He spectral series 2S1−nQ1 (n=3÷9, Q=S,P,D,…,n−1) and 2P1−nQ1 (n=3÷9, Q=S,P,D,…,n−1) in electric fields up to 1635 kV/cm. Apart from the allowed transitions with |ΔL|=1, the transitions with |ΔL|=0,2,3,…-without field strictly forbidden-were observed. Several He patterns become similar to hydrogen patterns, which means they are nearly symmetric and show in higher fields...
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Testing the Weibull distribution in road traffic losses analysis
PublicationThe paper presents an attempt of applying the Weibull distribution for the purpose of analysing road traffic losses (fatalities). The question it asks is whether reliability engineering methods can be applied for the analyses. If this is the case, what should be the interpretation of the numbers and terms? It was assumed that the losses generated by a malfunctioning road transport system are fatalities. Risk exposure to these losses...
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Hybrid Technique Combining the FDTD Method and Its Convolution Formulation Based on the Discrete Green's Function
PublicationIn this letter, a technique combining the finite-difference time-domain (FDTD) method and its formulation based on the discrete Green's function (DGF) is presented. The hybrid method is applicable to inhomogeneous dielectric structures that are mutually coupled with wire antennas. The method employs the surface equivalence theorem in the discrete domain to separate the problem into a dielectric domain simulated using the FDTD method...
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Problems of analytical determination of journal bearing bush fatigue strength estimates
PublicationProblems connected with determination of stress distribution in sliding layer of thinwalled bearing bushes, investigated in bearing fatigue test rigs, have been presented. Using an example of plain bearings tested in the fatigue machine SMOK (built at the Gdask University of Technology) problems with obtaining a convergence of iterative procedure for determining the fatigue strength estimators of bearing alloy surface layer are...
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Application of the discrete Green's function-based antenna simulations for excitation of the total-field/scattered-field interface in the FDTD method
PublicationIn this article, the discrete Green's function formulation of the finite-difference time-domain (DGF-FDTD) method is proposed for simulation of wire antennas irradiating inhomogeneous dielectric scatterers. Surface equivalence theorem in the discrete domain is used to separate the problem into an inhomogeneous domain and a wire antenna that are simulated with the use of FDTD and DGF-FDTD, respectively. Then, the excitation of the...
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Model of Volunteer Based Systems.
PublicationThere are two main approaches to processing tasks requiring high amounts of computational power. One approach is using clusters of mostly identical hardware, placed in dedicated locations. The other approach is outsourcing computing resources from large numbers of volunteers connected to the Internet. This chapter attempts to formulate a mathematical model of the volunteer based approach to distributed computations and apply it...
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Curlicues generated by circle homeomorphisms
PublicationWe investigate the curves in the complex plane which are generated by sequences of real numbers being the lifts of the points on the orbit of an orientation preserving circle homeomorphism. Geometrical properties of these curves such as boundedness, superficiality, local discrete radius of curvature are linked with dynamical properties of the circle homeomorphism which generates them: rotation number and its continued fraction...
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Quaternion Encryption Method for Image and Video Transmission
PublicationQuaternions are hyper-complex numbers of rank 4. They are often applied to mechanics in 3D space and are considered to be one of the best ways of representing rotations. In this paper a quaternion encryption method, based on algorithm by Nagase et al. (2004) has been proposed. According to a computer-based simulation the results of the performed research yield a high level of security, which is additionally strengthened by the...
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Modeling Volunteer Based Systems
PublicationThere are two main approaches to processing tasks requiring high amounts of computational power. One approach is using clusters of mostly identical hardware, placed in dedicated locations [1, 2, 3]. The other approach is outsourcing computing resources from large numbers of volunteers connected to the Internet [7]. This chapter presents an application of a mathematical model of the volunteer computing presented in Volume 1 of this...
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A Selection of Starting Points for Iterative Position Estimation Algorithms Using Feedforward Neural Networks
PublicationThis article proposes the use of a feedforward neural network (FNN) to select the starting point for the first iteration in well-known iterative location estimation algorithms, with the research objective of finding the minimum size of a neural network that allows iterative position estimation algorithms to converge in an example positioning network. The selected algorithms for iterative position estimation, the structure of the...
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Model Correction and Optimization Framework for Expedited EM-Driven Surrogate-Assisted Design of Compact Antennas
PublicationDesign of compact antennas is a numerically challenging process that heavily relies on electromagnetic (EM) simulations and numerical optimization algorithms. For reliability of simulation results, EM models of small radiators often include connectors which—despite being components with fixed dimensions—significantly contribute to evaluation cost. In this letter, a response correction method for antenna models without connector,...
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On the Structure of Time in Computational Semantics of a Variable-Step Solver for Hybrid Behavior Analysis
PublicationHybrid dynamic systems combine continuous and discrete behavior. Often, computational approaches are employed to derive behaviors that approximate the analytic solution. An important part of this is the approximation of differential equation behavior by numerical integration. The accuracy and computational efficiency of the integration usually depend on the complexity of the method and its implicated approximation errors, especially...
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Optimal shape design of multi-element trawl-doors using local surrogate models
PublicationTrawl-doors have a large influence on the fuel consumption of fishing vessels. Design and optimiza-tion of trawl-doors using computational models are a key factor in minimizing the fuel consump-tion. This paper presents an optimization algorithm for the shape design of trawl-door shapes using computational fluid dynamic (CFD) models. Accurate CFD models are computationally expensive. Therefore, the direct use of traditional optimization...
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Buckling and shape control of prestressable trusses using optimum number of actuators
PublicationThis paper describes a method to control the nodal displacement of prestressable truss structures within the desired domains. At the same time, the stress in all members is unleashed to take any value between the allowable tensile stress and critical buckling stress. The shape and stresses are controlled by actuating the most active members. The technique considers the members’ initial crookedness, residual stresses, and slenderness...
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Selected elements of the payment cards system in Poland
PublicationThe following article describes the current situation of the selected elements of the payment cards system in Poland. The first part of the paper include the most common definition as well as the abbreviated history of payment cards implementation in Poland. Next, the author presents the key numbers related to the nowadays situation on the market together with benefits of using the payment cards in the whole economic system. At...
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Hydration of urea and its derivatives - Volumetric and compressibility studies
PublicationThe densities and sound velocities at T = (288.15, 293.15, 298.15, 303.15 and 308.15) K have been measured for aqueous solutions of urea, N,N-dimethylurea, N,N-diethylurea, N-propylurea, N-butylurea. From these data the apparent molar volumes, V the apparent molar isentropic compressions, KS,, and the Passynski solvation numbers of solutes have been determined. The concentration dependencies of the calculated quantities, their...
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Seagrass vegetation and meiofauna enhance the bacterial abundance in the Baltic Sea sediments (Puck Bay)
PublicationThis study presents the first report on bacterial communities in the sediments of eelgrass (Zostera marina) meadows in the shallow southern Baltic Sea (Puck Bay). Total bacterial cell numbers (TBNs) and bacteria biomass (BBM) assessed with the use of epifluorescence microscope and Norland’s formula were compared between bare and vegetated sediments at two localities and in two sampling summer months. Significantly higher TBNs and...
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Three levels of fail-safe mode in MPI I/O NVRAM distributed cache
PublicationThe paper presents architecture and design of three versions for fail-safe data storage in a distributed cache using NVRAM in cluster nodes. In the first one, cache consistency is assured through additional buffering write requests. The second one is based on additional write log managers running on different nodes. The third one benefits from synchronization with a Parallel File System (PFS) for saving data into a new file which...
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Arterial cannula shape optimization by means of the rotational firefly algorithm
PublicationThe article presents global optimization results of arterial cannula shapes by means of the newly modified firefly algorithm. The search for the optimal arterial cannula shape is necessary in order to minimize losses and prepare the flow that leaves the circulatory support system of a ventricle (i.e. blood pump) before it reaches the heart. A modification of the standard firefly algorithm, the so-called rotational firefly algorithm,...
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Considerations about the applicability of the Reynolds equation for analyzing high-speed near field levitation phenomena
Publicationequation for analyzing near field levitation (NFL) phenomena. Two separate approaches were developed, experimentally verified, and applied to meet the research objective. One was based on the Reynolds equation and the other was based on general conservation equations for fluid flow solved using computational fluid dynamic (CFD). Comparing the calculation results revealed that, for certain operating conditions, differences in the...
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On proper (1,2)‐dominating sets in graphs
PublicationIn 2008, Hedetniemi et al. introduced the concept of (1,)-domination and obtained some interesting results for (1,2) -domination. Obviously every (1,1) -dominating set of a graph (known as 2-dominating set) is (1,2) -dominating; to distinguish these concepts, we define a proper (1,2) -dominating set of a graph as follows: a subset is a proper (1,2) -dominating set of a graph if is (1,2) -dominating and it is not a (1,1) -dominating...
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Benchmarking Parallel Chess Search in Stockfish on Intel Xeon and Intel Xeon Phi Processors
PublicationThe paper presents results from benchmarking the parallel multithreaded Stockfish chess engine on selected multi- and many-core processors. It is shown how the strength of play for an n-thread version compares to 1-thread version on both Intel Xeon and latest Intel Xeon Phi x200 processors. Results such as the number of wins, losses and draws are presented and how these change for growing numbers of threads. Impact of using particular...
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On the independence number of some strong products of cycle-powers
PublicationIn the paper we give some theoretical and computational results on the third strong power of cycle-powers, for example, we have found the independence numbers alpha((C^2_10)^⊠3) = 30 and alpha((C^4 _14)^⊠3) = 14. A number of optimizations have been introduced to improve the running time of our exhaustive algorithm used to establish the independence number of the third strong power of cycle-powers. Moreover, our results establish...
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Non-Diophantine Arithmetics in Mathematics, Physics and Psychology
PublicationFor a long time, all thought there was only one geometry — Euclidean geometry. Nevertheless, in the 19th century, many non-Euclidean geometries were discovered. It took almost two millennia to do this. This was the major mathematical discovery and advancement of the 19th century, which changed understanding of mathematics and the work of mathematicians providing innovative insights and tools for mathematical research and applications...
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Experimental certification of more than one bit of quantum randomness in the two inputs and two outputs scenario
PublicationOne of the striking properties of quantum mechanics is the occurrence of the Bell-type non-locality. They are a fundamental feature of the theory that allows two parties that share an entangled quantum system to observe correlations stronger than possible in classical physics. In addition to their theoretical significance, non-local correlations have practical applications, such as device-independent randomness generation, providing...
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Deep Learning Optimization for Edge Devices: Analysis of Training Quantization Parameters
PublicationThis paper focuses on convolution neural network quantization problem. The quantization has a distinct stage of data conversion from floating-point into integer-point numbers. In general, the process of quantization is associated with the reduction of the matrix dimension via limited precision of the numbers. However, the training and inference stages of deep learning neural network are limited by the space of the memory and a...
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Certified domination
PublicationImagine that we are given a set D of officials and a set W of civils. For each civil x ∈ W, there must be an official v ∈ D that can serve x, and whenever any such v is serving x, there must also be another civil w ∈ W that observes v, that is, w may act as a kind of witness, to avoid any abuse from v. What is the minimum number of officials to guarantee such a service, assuming a given social network? In this paper, we introduce...
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A collection of directed graphs for the minimum cycle mean weight computation
Open Research DataThis dataset contains definitions of the 16 directed graphs with weighted edges that were described in the following paper: Paweł Pilarczyk, A space-efficient algorithm for computing the minimum cycle mean in a directed graph, Journal of Mathematics and Computer Science, 20 (2020), no. 4, 349--355, DOI: 10.22436/jmcs.020.04.08, URL: http://dx.doi.org/10.22436/jmcs.020.04.08 These...
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Bistability in a One-Dimensional Model of a Two-Predators-One-Prey Population Dynamics System
PublicationIn this paper, we study a classical two-predators-one-prey model. The classical model described by a system of three ordinary differential equations can be reduced to a one-dimensional bimodalmap. We prove that this map has at most two stable periodic orbits. Besides, we describe the bifurcation structure of the map. Finally, we describe a mechanism that leads to bistable regimes. Taking this mechanism into account, one can easily...
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Modelling fatalities on regional road networks
PublicationDuring the last decade Poland’s road fatalities went down by 44%. The trend differs from region to region. Effective road safetymanagement in regions requires tools for forecasting road safety measures and identifying factors influencing road fatality numbers. Mathematical models can provide such tools. They take into account local characteristics such as: demography, economy, infrastructure and motorization. Such models could...
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Invariant Measures for Uncountable Random Interval Homeomorphisms
PublicationA necessary and sufficient condition for the iterated function system { f (·, ω) | ω ∈ } with probability P to have exactly one invariant measure μ∗ with μ∗((0, 1)) = 1 is given. The main novelty lies in the fact that we only require the transformations f (·, ω) to be increasing homeomorphims, without any smoothness condition, nei- ther we impose conditions on the cardinality of . In particular, positive Lyapunov exponents conditions...
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Multi-agent large-scale parallel crowd simulation
PublicationThis paper presents design, implementation and performance results of a new modular, parallel, agent-based and large scale crowd simulation environment. A parallel application, implemented with C and MPI, was implemented and run in this parallel environment for simulation and visualization of an evacuation scenario at Gdansk University of Technology, Poland and further in the area of districts of Gdansk. The application uses a...
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Benchmarking Scalability and Security Configuration Impact for A Distributed Sensors-Server IOT Use Case
PublicationInternet of Things has been getting more and more attention and found numerous practical applications. Especially important in this context are performance, security and ability to cope with failures. Especially crucial is to find good trade-off between these. In this article we present results of practical tests with multiple clients representing sensors sending notifications to an IoT middleware – DeviceHive. We investigate performance...
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On trees attaining an upper bound on the total domination number
PublicationA total dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D. The total domination number of a graph G, denoted by γ_t(G), is the minimum cardinality of a total dominating set of G. Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International Journal of Graphs and Combinatorics 1 (2004), 69-75] established the following upper bound on the total domination...
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FPGA realization of an improved alpha max plus beta min algorithm
PublicationThe generalized improved version of the alpha max plus beta min square-rooting algorithm and its realization in the Field Programmable Gate Array (FPGA) are presented. The algorithm computes the square root to calculate the approximate magnitude of a complex sample. It is especially useful for pipelined calculations in the DSP. In case of four approximation regions it is possible to reduce the peak error form 3.95% to 0.33%. This...
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On the differential effect of temperature on the Nusselt-Rayleigh relationship in free convection
PublicationThe aim of and inspiration behind this paper was to explain the reasons, also observed by other researchers, of the discrepancy in the results of experimental free convection, which for small Rayleigh and Nusselt numbers in the initial phase of research can sometimes reach several hundred percent. These discrepancies decrease with increasing heating power and plate surface temperature, in proportion to the increase in Ra and Nu,...
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Robust four-node elements based on Hu–Washizu principle for nonlinear analysis of Cosserat shells
PublicationMixed 4-node shell elements with the drilling rotation and Cosserat-type strain measures based onthe three-field Hu–Washizu principle are proposed. In the formulation, apart from displacement and rotationfields, both strain and stress resultant fields are treated as independent. The elements are derived in the frame-work of a general nonlinear 6-parameter shell theory dedicated to the analysis of multifold irregular shells.The...