Procedures for the Verification and Validation of Working Models for Structural Shells

2005 ◽  
Vol 72 (6) ◽  
pp. 907-915 ◽  
Author(s):  
Barna A. Szabo ◽  
Daniel E. Muntges
Keyword(s):  
Mathematical Model ◽  
Practical Problem ◽  
Expert Knowledge ◽  
Displacement Vector ◽  
Three Dimensional ◽  
Verification And Validation ◽  
Working Models ◽  
Solid Bodies ◽  
Simplified Mathematical Model ◽  
Transverse Variation

Shell-like structures are viewed as fully three-dimensional solid bodies that allow the imposition of restrictions on the transverse variation of displacement vector components in certain regions. An important practical problem is to select a simplified mathematical model for a particular application so that the simplifications do not affect the data of interest significantly. This involves application of expert knowledge aided by virtual and∕or physical experimentation. An example is presented.

An Eight-Node Hexahedral Finite Element with Rotational DOFs for Elastoplastic Applications

2019 ◽  
Vol 11 (1) ◽  
pp. 54-66
Author(s):  
Ayoub Ayadi ◽  
Kamel Meftah ◽  
Lakhdar Sedira ◽  
Hossam Djahara
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Plastic Zone ◽  
Displacement Vector ◽  
Small Strain ◽  
Benchmark Problems ◽  
Plasticity Model ◽  
Vector Approximation ◽  
Calculation Code

Abstract In this paper, the earlier formulation of the eight-node hexahedral SFR8 element is extended in order to analyze material nonlinearities. This element stems from the so-called Space Fiber Rotation (SFR) concept which considers virtual rotations of a nodal fiber within the element that enhances the displacement vector approximation. The resulting mathematical model of the proposed SFR8 element and the classical associative plasticity model are implemented into a Fortran calculation code to account for small strain elastoplastic problems. The performance of this element is assessed by means of a set of nonlinear benchmark problems in which the development of the plastic zone has been investigated. The accuracy of the obtained results is principally evaluated with some reference solutions.

A Real-Time Mathematical Model for Three-Dimensional Tidal Flow and Water Quality

1991 ◽  
Vol 24 (6) ◽  
pp. 171-177 ◽  
Author(s):  
Zeng Fantang ◽  
Xu Zhencheng ◽  
Chen Xiancheng
Keyword(s):  
Mathematical Model ◽  
Water Quality ◽  
Real Time ◽  
Control Volume ◽  
Tidal Flow ◽  
Three Dimensional ◽  
River Estuary ◽  
Pearl River Estuary ◽  
Practical Application ◽  
The Pearl River

A real-time mathematical model for three-dimensional tidal flow and water quality is presented in this paper. A control-volume-based difference method and a “power interpolation distribution” advocated by Patankar (1984) have been employed, and a concept of “separating the top-layer water” has been developed to solve the movable boundary problem. The model is unconditionally stable and convergent. Practical application of the model is illustrated by an example for the Pearl River Estuary.

scholarly journals Organ motion in linac-based SBRT for glottic cancer

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Annarita Perillo ◽  
Valeria Landoni ◽  
Alessia Farneti ◽  
Giuseppe Sanguineti
Keyword(s):  
Early Stage ◽  
Displacement Vector ◽  
Thyroid Cartilage ◽  
Three Dimensional ◽  
Target Volume ◽  
Glottic Cancer ◽  
Organ Motion ◽  
Delivery Times ◽  
Significant Difference ◽  
Pre Treatment

Abstract Purpose The purpose of this study is to evaluate inter- and intra-fraction organ motion as well as to quantify clinical target volume (CTV) to planning target volume (PTV) margins to be adopted in the stereotactic treatment of early stage glottic cancer. Methods and materials Stereotactic body radiotherapy (SBRT) to 36 Gy in 3 fractions was administered to 23 patients with early glottic cancer T1N0M0. Patients were irradiated with a volumetric intensity modulated arc technique delivered with 6 MV FFF energy. Each patient underwent a pre-treatment cone beam computed tomography (CBCT) to correct the setup based on the thyroid cartilage position. Imaging was repeated if displacement exceeded 2 mm in any direction. CBCT imaging was also performed after each treatment arc as well as at the end of the delivery. Swallowing was allowed only during the beam-off time between arcs. CBCT images were reviewed to evaluate inter- and intra-fraction organ motion. The relationships between selected treatment characteristics, both beam-on and delivery times as well as organ motion were investigated. Results For the population systematic (Ʃ) and random (σ) inter-fraction errors were 0.9, 1.3 and 0.6 mm and 1.1, 1.3 and 0.7 mm in the left-right (X), cranio-caudal (Y) and antero-posterior (Z) directions, respectively. From the analysis of CBCT images acquired after treatment, systematic (Ʃ) and random (σ) intra-fraction errors resulted 0.7, 1.6 and 0.7 mm and 1.0, 1.5 and 0.6 mm in the X, Y and Z directions, respectively. Margins calculated from the intra-fraction errors were 2.4, 5.1 and 2.2 mm in the X, Y and Z directions respectively. A statistically significant difference was found for the displacement in the Z direction between patients irradiated with > 2 arcs versus ≤ 2 arcs, (MW test, p = 0.038). When analyzing mean data from CBCT images for the whole treatment, a significant correlation was found between the time of delivery and the three dimensional displacement vector (r = 0.489, p = 0.055), the displacement in the Y direction (r = 0.553, p = 0.026) and the subsequent margins to be adopted (r = 0.626, p = 0.009). Finally, displacements and the subsequent margins to be adopted in Y direction were significantly greater for treatments with more than 2 arcs (MW test p = 0.037 and p = 0.019, respectively). Conclusions In the setting of controlled swallowing during treatment delivery, intra-fraction motion still needs to be taken into account when planning with estimated CTV to PTV margins of 3, 5 and 3 mm in the X, Y and Z directions, respectively. Selected treatments may require additional margins.

Research on cargo-loading optimization based on genetic and fuzzy integration

2021 ◽  
Vol 40 (4) ◽  
pp. 8493-8500
Author(s):  
Yanwei Du ◽  
Feng Chen ◽  
Xiaoyi Fan ◽  
Lei Zhang ◽  
Henggang Liang
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Three Dimensional ◽  
Distribution Center ◽  
Long Time ◽  
Low Efficiency ◽  
Decision Making Model ◽  
The Mathematical Model ◽  
Loading Scheme

With the increase of the number of loaded goods, the number of optional loading schemes will increase exponentially. It is a long time and low efficiency to determine the loading scheme with experience. Genetic algorithm is a search heuristic algorithm used to solve optimization in the field of computer science artificial intelligence. Genetic algorithm can effectively select the optimal loading scheme but unable to utilize weight and volume capacity of cargo and truck. In this paper, we propose hybrid Genetic and fuzzy logic based cargo-loading decision making model that focus on achieving maximum profit with maximum utilization of weight and volume capacity of cargo and truck. In this paper, first of all, the components of the problem of goods stowage in the distribution center are analyzed systematically, which lays the foundation for the reasonable classification of the problem of goods stowage and the establishment of the mathematical model of the problem of goods stowage. Secondly, the paper abstracts and defines the problem of goods loading in distribution center, establishes the mathematical model for the optimization of single car three-dimensional goods loading, and designs the genetic algorithm for solving the model. Finally, Matlab is used to solve the optimization model of cargo loading, and the good performance of the algorithm is verified by an example. From the performance evaluation analysis, proposed the hybrid system achieve better outcomes than the standard SA model, GA method, and TS strategy.

scholarly journals Application of the erosion algorithm in modeling of structures behavior under impulse loads

2019 ◽  
Vol 221 ◽  
pp. 01003
Author(s):  
Pavel Radchenko ◽  
Stanislav Batuev ◽  
Andrey Radchenko
Keyword(s):  
Finite Element ◽  
High Velocity ◽  
Three Dimensional ◽  
Computer Software ◽  
Dynamic Loads ◽  
Complex Structures ◽  
Numerical Studies ◽  
Contact Surfaces ◽  
Fracture Of Materials ◽  
Solid Bodies

The paper presents results of applying approach to simulation of contact surfaces fracture under high velocity interaction of solid bodies. The algorithm of erosion -the algorithm of elements removing, of new surface building and of mass distribution after elements fracture at contact boundaries is consider. The results of coordinated experimental and numerical studies of fracture of materials under impact are given. Authors own finite element computer software program EFES, allowing to simulate a three-dimensional setting behavior of complex structures under dynamic loads, has been used for the calculations.

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