S6801 User's Guide. Version 1.0. Static Analysis of Plane Frame and Truss Structures

1989 ◽  
Author(s):  
Frank R. Johnson
Keyword(s):  
Static Analysis ◽  
Truss Structures ◽  
Plane Frame

Static Analysis of Fe Discretized Structures With Bounded Uncertainties via Interval Method

2009 ◽  
Author(s):  
Nicola Impollonia ◽  
Giuseppe Muscolino
Keyword(s):  
Static Analysis ◽  
Interval Analysis ◽  
Stiffness Matrix ◽  
Probabilistic Method ◽  
Probabilistic Approach ◽  
Great Accuracy ◽  
Truss Structures ◽  
Interval Model ◽  
Global Stiffness Matrix ◽  
Bounded Uncertainties

The uncertainty presents in many engineering analysis is usually modeled by probabilistic approach. It is now largely recognized that the probabilistic approach often cannot be applied to describe structural uncertainty; indeed, it requires a wealth of data, often unavailable, to define the probability density function of the uncertainties. Alternatively non-probabilistic method can be adopted. In this framework, the interval model seems today the most suitable analytical tool. The interval model is derived from the interval analysis, in which the number is treated as an interval variable with lower and upper bounds. However, the application of the interval analysis in classical form can result in a severe overestimation of the uncertainty of the output. In this paper the limit of interval analysis is overcome by deriving an alternative solution, in the framework of linear static analysis of finite element modeled structures with uncertain-but-bounded parameters. The proposed procedure is based on the factorization of the elemental stiffness matrix following the unimodal components concept, which allows a non conventional assembly of the global stiffness matrix, and on the inversion of the assembled stiffness matrix by an interval-valued Sherman-Morrison formula. Numerical results on truss structures evidence the great accuracy of the proposed approach.

Deflection Estimates Using the Virtual Work Principle

1984 ◽  
Vol 8 (3) ◽  
pp. 133-137
Author(s):  
Robert Piché
Keyword(s):  
Static Analysis ◽  
Error Bounds ◽  
Upper Bound ◽  
Virtual Work ◽  
Complementary Energy ◽  
Virtual Work Principle ◽  
Plane Frame ◽  
Rigid Plane ◽  
Indeterminate Structures

Well-established methods of approximate static analysis for linear statically indeterminate structures are combined with the method of virtual work to calculate approximate deflections. The method is more general than the method of minimum complementary energy, since deflections may be estimated at any point of the structure, and there may be any number of loads applied (including distributed loads). Error bounds are derived, and sufficient (verifiable) conditions for the method to yield upper-bound estimates are proved. Finally, two examples are worked out: a double-braced truss and a rigid plane frame.

Quadratic Mode Shape Components From Linear Finite Element Analysis

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
L. H. van Zyl ◽  
E. H. Mathews
Keyword(s):  
Finite Element ◽  
Static Analysis ◽  
Mode Shape ◽  
Turbine Blades ◽  
Rotor Blades ◽  
Nonlinear Static Analysis ◽  
Truss Structures ◽  
Element Analysis ◽  
Quadratic Mode ◽  
Nonlinear Static

Points on a vibrating structure move along curved paths rather than straight lines; however, this is largely ignored in modal analysis. Applications where the curved path of motion cannot be ignored include beamlike structures in rotating systems, e.g., helicopter rotor blades, compressor and turbine blades, and even robot arms. In most aeroelastic applications the curvature of the motion is of no consequence. The flutter analysis of T-tails is one notable exception due to the steady-state trim load on the horizontal stabilizer. Modal basis buckling analyses can also be performed when taking the curved path of motion into account. The effective application of quadratic mode shape components to capture the essential kinematics has been shown by several researchers. The usual method of computing the quadratic mode shape components for general structures employs multiple nonlinear static analyses for each component. It is shown here how the quadratic mode shape components for general structures can be obtained using linear static analysis. The derivation is based on energy principles. Only one linear static load case is required for each quadratic component. The method is illustrated for truss structures and applied to nonlinear static analyses of a linear and a geometrically nonlinear structure. The modal method results are compared to finite element nonlinear static analysis results. The proposed method for calculating quadratic mode shape components produces credible results and offers several advantages over the earlier method, viz., the use of linear analysis instead of nonlinear analysis, fewer load cases per quadratic mode shape component, and user-independence.

scholarly journals Seismic performance of deep excavation restrained by guardian truss structures system using quasi-static approach

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
Mahdi Maleki ◽  
Ali Nabizadeh
Keyword(s):  
Static Analysis ◽  
Safety Factor ◽  
Seismic Analysis ◽  
Horizontal Displacement ◽  
Friction Angle ◽  
Truss Structures ◽  
Horizontal Distance ◽  
Deep Excavation ◽  
Static Approach ◽  
The Guardian

AbstractThe control of deformation and stability of the deep excavation walls under seismic and static loads is one of the most important issues in geotechnical engineering. Therefore, in the present study, using the finite element method and taking into account Hardening soil's behavioural model, the effect of different parameters affecting the performance of the deep excavation walls with the guardian truss structures using quasi-static analysis and its comparison with static analysis has been performed. According to the most important results, increasing in the geotechnical parameters of soil such as cohesion, friction angle and elastic modulus will reduce the maximum horizontal displacement in the vertical trench wall. Besides, the maximum settling in the adjacent ground and the maximum swelling in the bottom of the excavation will be reduced. In this way, the improvement in soil resistance parameters will increase the safety factor. Conversely, by increasing the horizontal distance between the trusses, the maximum horizontal displacement and the maximum settling in the adjacent ground and the maximum swelling in the bottom of the excavation will increase and the safety factor will be reduced. Also, the findings from this research show that by increasing the horizontal seismic acceleration coefficient (Kh) and as the construction stages progress, the maximum horizontal displacement of the wall, the maximum settling of the adjacent ground of the wall and the maximum swelling on the bottom of the trench increase and the safety factor will decrease. As well as, the results obtained from the quasi-static seismic analysis of the vertical trench restrained by the guardian truss structure such as the maximum horizontal displacement of the vertical trench wall and the maximum settling in the adjacent ground and the maximum swelling of the bottom of the excavation are much more than the static analysis.

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