Thrust Surface Method: An innovative approach for the three-dimensional lower bound Limit Analysis of masonry vaults

2020 ◽  
Vol 202 ◽  
pp. 109846 ◽  
Author(s):  
Aguinaldo Fraddosio ◽  
Nicola Lepore ◽  
Mario Daniele Piccioni
Keyword(s):  
Lower Bound ◽  
Limit Analysis ◽  
Three Dimensional ◽  
Innovative Approach ◽  
Surface Method ◽  
Masonry Vaults ◽  
Lower Bound Limit Analysis

A fundamental class of stress elements in lower bound limit analysis

2020 ◽  
Vol 476 (2243) ◽  
pp. 20200425
Author(s):  
Athanasios Makrodimopoulos
Keyword(s):  
Lower Bound ◽  
Limit Analysis ◽  
Polynomial Interpolation ◽  
Yield Criterion ◽  
Bernstein Polynomials ◽  
Three Dimensional ◽  
Bound Theorem ◽  
The One ◽  
Uniformly Distributed Loads ◽  
Lower Bound Limit Analysis

There is a major restriction in the formulation of rigorous lower bound limit analysis by means of the finite-element method. Once the stress field has been discretized, the yield criterion and the equilibrium conditions must be applied at a finite number of points so that they are satisfied everywhere throughout the discretized structure. Until now, only the linear stress elements fulfil this requirement for several types of loads and structural conditions. However, there are also standard types of problems, like the one of plates under uniformly distributed loads, where the implementation of the lower bound theorem is still not possible. In this paper, it is proven for the first time that there is a class of stress interpolation elements which fulfils all the requirements of the lower bound theorem. Moreover, there is no upper restriction of the polynomial interpolation order. The efficiency is examined through plane strain, plane stress and Kirchhoff plate examples. The generalization to three-dimensional and other structural conditions is also straightforward. Thus, this interpolation scheme which is based on the Bernstein polynomials is expected to play a fundamental role in future developments and applications.

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