A method for the derivation of load effect envelopes based on statistical considerations

1993 ◽  
Vol 20 (2) ◽  
pp. 201-209
Author(s):  
Eugene J. O'Brien ◽  
Robert E. Loov
Keyword(s):  
Structural Analysis ◽  
Three Dimensional ◽  
Elastic Analysis ◽  
Two Dimensional ◽  
Statistical Parameters ◽  
Simple Method ◽  
Load Effect ◽  
Linear Elastic ◽  
Derived Design ◽  
Usual Process

A simple method is proposed as a substitute for the usual process of factoring loads, performing a linear elastic analysis, and determining an envelope of the results. The method is based on statistical principles, but only a minimum knowledge of statistics is required for its use. It involves conventional structural analysis followed by some processing of the results which could readily be incorporated into existing computer programs.The practice of performing two-dimensional analyses on parts of three-dimensional structures is possible with the proposed approach. The implications are clarified and the necessary statistical parameters are derived.Deterministically derived design envelopes represent all the extremes of loading that can reasonably be considered. The envelopes found by the new method not only reflect loading variations but also consider their relative probabilities of occurrence so that excursions beyond the envelope are expected to be equally infrequent along the entire length of the structure. Inconsistencies inherent in the conventional approach are highlighted by comparison with the proposed method for a number of examples. Key words: probabilistic, safety, load, imposed load, load effect envelope, building.

scholarly journals Two-Dimensional Visualization of the Three-Dimensional Planned Sacroiliac Screw Corridor with the Slice Fusion Method

2021 ◽  
Vol 10 (2) ◽  
pp. 184
Author(s):  
Maximilian Kerschbaum ◽  
Siegmund Lang ◽  
Florian Baumann ◽  
Volker Alt ◽  
Michael Worlicek
Keyword(s):  
Pelvic Ring ◽  
Three Dimensional ◽  
Fusion Method ◽  
Two Dimensional ◽  
Posterior Pelvic Ring ◽  
Simple Method ◽  
Sacroiliac Screw ◽  
Screw Insertion ◽  
Multiplanar Reconstructions ◽  
Screw Position

Insertion of sacro-iliac (SI) screws for stabilization of the posterior pelvic ring without intraoperative navigation or three-dimensional imaging can be challenging. The aim of this study was to develop a simple method to visualize the ideal SI screw corridor, on lateral two-dimensional images, corresponding to the lateral fluoroscopic view, used intraoperatively while screw insertion, to prevent neurovascular injury. We used multiplanar reconstructions of pre- and postoperative computed tomography scans (CT) to determine the position of the SI corridor. Then, we processed the dataset into a lateral two-dimensional slice fusion image (SFI) matching head and tip of the screw. Comparison of the preoperative SFI planning and the screw position in the postoperative SFI showed reproducible results. In conclusion, the slice fusion method is a simple technique for translation of three-dimensional planned SI screw positioning into a two-dimensional strict lateral fluoroscopic-like view.

Implementation of p and h-p Versions of the Finite Element Method

1992 ◽  
Author(s):  
Ye-Chen Lai ◽  
Timothy C. S. Liang ◽  
Zhenxue Jia
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Analysis ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Shape Functions ◽  
Linear Elastic ◽  
Finite Element Software ◽  
Analysis Process ◽  
Adaptive Analysis

Abstract Based on hierarchic shape functions and an effective convergence procedure, the p-version and h-p adaptive analysis capabilities were incorporated into a finite element software system, called COSMOS/M. The range of the polynomial orders can be varied from 1 to 10 for two dimensional linear elastic analysis. In the h-p adaptive analysis process, a refined mesh are first achieved via adaptive h-refinement. The p-refinement is then added on to the h-version designed mesh by uniformly increasing the degree of the polynomials. Some numerical results computed by COSMOS/M are presented to illustrate the performance of these p and h-p analysis capabilities.

scholarly journals Membrane analogy for multi-material bars under torsion

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190124 ◽  
Author(s):  
Laura Galuppi ◽  
Gianni Royer-Carfagni
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Elastic Problem ◽  
Two Dimensional ◽  
Torsion Problem ◽  
Linear Elastic ◽  
Physical Apparatus

Prandtl's membrane analogy for the torsion problem of prismatic homogeneous bars is extended to multi-material cross sections. The linear elastic problem is governed by the same equations describing the deformation of an inflated membrane, differently tensioned in regions that correspond to the domains hosting different materials in the bar cross section, in a way proportional to the inverse of the material shear modulus. Multi-connected cross sections correspond to materials with vanishing stiffness inside the holes, implying infinite tension in the corresponding portions of the membrane. To define the interface constrains that allow to apply such a state of prestress to the membrane, a physical apparatus is proposed, which can be numerically modelled with a two-dimensional mesh implementable in commercial finite-element model codes. This approach presents noteworthy advantages with respect to the three-dimensional modelling of the twisted bar.

scholarly journals Parallel computations in nonlinear solid mechanics using adaptive finite element and meshless methods

2016 ◽  
Vol 33 (4) ◽  
pp. 1161-1191 ◽  
Author(s):  
Zahur Ullah ◽  
Will Coombs ◽  
C Augarde
Keyword(s):  
Finite Element ◽  
Parallel Algorithms ◽  
Meshless Method ◽  
Three Dimensional ◽  
Meshless Methods ◽  
Basis Functions ◽  
Two Dimensional ◽  
Content Type ◽  
Linear Elastic ◽  
Geometrical Nonlinearities

Purpose – A variety of meshless methods have been developed in the last 20 years with an intention to solve practical engineering problems, but are limited to small academic problems due to associated high computational cost as compared to the standard finite element methods (FEM). The purpose of this paper is to develop an efficient and accurate algorithms based on meshless methods for the solution of problems involving both material and geometrical nonlinearities. Design/methodology/approach – A parallel two-dimensional linear elastic computer code is presented for a maximum entropy basis functions based meshless method. The two-dimensional algorithm is subsequently extended to three-dimensional adaptive nonlinear and three-dimensional parallel nonlinear adaptively coupled finite element, meshless method cases. The Prandtl-Reuss constitutive model is used to model elasto-plasticity and total Lagrangian formulations are used to model finite deformation. Furthermore, Zienkiewicz and Zhu and Chung and Belytschko error estimation procedure are used in the FE and meshless regions of the problem domain, respectively. The message passing interface library and open-source software packages, METIS and MUltifrontal Massively Parallel Solver are used for the high performance computation. Findings – Numerical examples are given to demonstrate the correct implementation and performance of the parallel algorithms. The agreement between the numerical and analytical results in the case of linear elastic example is excellent. For the nonlinear problems load-displacement curve are compared with the reference FEM and found in a very good agreement. As compared to the FEM, no volumetric locking was observed in the case of meshless method. Furthermore, it is shown that increasing the number of processors up to a given number improve the performance of parallel algorithms in term of simulation time, speedup and efficiency. Originality/value – Problems involving both material and geometrical nonlinearities are of practical importance in many engineering applications, e.g. geomechanics, metal forming and biomechanics. A family of parallel algorithms has been developed in this paper for these problems using adaptively coupled finite element, meshless method (based on maximum entropy basis functions) for distributed memory computer architectures.

Three-dimensional deformations in a single-lap joint

1994 ◽  
Vol 29 (2) ◽  
pp. 137-145 ◽  
Author(s):  
M Y Tsai ◽  
J Morton
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Stress Distributions ◽  
Lap Joint ◽  
Displacement Fields ◽  
Element Analysis ◽  
Linear Elastic ◽  
Non Linear ◽  
Linear Effects ◽  
Peel Stress

The three-dimensional nature of the state of deformation in a single-lap test specimen is investigated in a linear elastic finite element analysis in which the boundary conditions account for the geometrically non-linear effects. The validity of the model is demonstrated by comparing the resulting displacement fields with those obtained from a moiré inteferometry experiment. The three-dimensional adherend and adhesive stress distributions are calculated and compared with those from a two-dimensional non-linear numerical analysis, Goland and Reissner's solution, and experimental measurements. The nature of the three-dimensional mechanics is described and discussed in detail. It is shown that three-dimensional regions exists in the specimen, where the adherend and adhesive stress distributions in the overlap near (and especially on) the free surface are quite different from those occurring in the interior. It is also shown that the adhesive peel stress is extremely sensitive to this three-dimensional effect, but the adhesive shear is not. It is also observed that the maximum value of the peel stress occurs at the end of the overlap in the central two-dimensional core region, rather than at the corners where the three-dimensional effects are found. The extent of three-dimensional regions is also quantified.

scholarly journals Extrinsic Calibration of Multiple Two-Dimensional Laser Rangefinders Based on a Trihedron

Sensors ◽  
2020 ◽  
Vol 20 (7) ◽  
pp. 1837 ◽  
Author(s):  
Fei Zhu ◽  
Yuchun Huang ◽  
Zizhu Tian ◽  
Yaowei Ma
Keyword(s):  
Autonomous Vehicles ◽  
Laser Scanning ◽  
Mobile Robotics ◽  
Three Dimensional ◽  
Point Problem ◽  
Two Dimensional ◽  
Simple Method ◽  
Extrinsic Calibration ◽  
Dimensional Reconstruction ◽  
Special Pattern

Multiple two-dimensional laser rangefinders (LRFs) are applied in many applications like mobile robotics, autonomous vehicles, and three-dimensional reconstruction. The extrinsic calibration between LRFs is the first step to perform data fusion and practical application. In this paper, we proposed a simple method to calibrate LRFs based on a corner composed of three mutually perpendicular planes. In contrast to other methods that require a special pattern or assistance from other sensors, the trihedron corner needed in this method is common in daily environments. In practice, we can adjust the position of the LRFs to observe the corner until the laser scanning plane intersects with three planes of the corner. Then, we formed a Perspective-Three-Point problem to solve the position and orientation of each LRF at the common corner coordinate system. The method was validated with synthetic and real experiments, showing better performance than existing methods.

“Exact” Three-Dimensional Linear and Nonlinear Seismic Analysis of Structures with Two-Dimensional Models

2003 ◽  
Vol 19 (4) ◽  
pp. 897-912 ◽  
Author(s):  
Michael Mehrain ◽  
Farzad Naeim
Keyword(s):  
Structural Analysis ◽  
Nonlinear Analysis ◽  
Seismic Analysis ◽  
Three Dimensional ◽  
Modeling Technique ◽  
Two Dimensional ◽  
Single Model ◽  
Relative Ease ◽  
Conventional Analysis ◽  
Linear And Nonlinear

This paper presents a modeling technique by which a complete three-dimensional (3-D) structural analysis of a structure can be performed using two-dimensional (2-D) models, and hence 2-D software. The approach includes the effect of torsion, walls perpendicular and inclined to the direction of motion as well as walls with L, T, and H shapes in plan. Diaphragm displacements are easily modeled. The method can be used with linear and nonlinear analysis. Nonlinearity in the diaphragms can also be modeled with relative ease. Furthermore, unlike the conventional analysis that requires two 2-D models, one in each direction of motion, to model the 3-D structure, this approach requires only a single model.

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