The Collapse Loads of Softening Elastoplastic Trusses
Date Issued
2007
Date
2007
Author(s)
Sung, Shin-Jang
DOI
zh-TW
Abstract
In the conventional limit analysis, only can perfect plasticity be dealt with. However, softening structures exist all over the world and they should be considered. Therefore, it is important to loose this restriction.
At first, a general material model is introduced. From it, we derive a generalized linearly softening model which can be specialized to be a softening truss model.
The equivalent optimization problem is also carried out here. Then, the problem of calculating the collapse load in the form of MPEC(mathmatical programming with equilibrium constraints) is developed by redefining the collapse load as maximum external work of the structure. We find out that the whole process of calculation, including the generalized model, is a nonlinear programming problem. The original equilibrium constraints are actually the KKT conditions of the nonlinear programming problem.
To enlarge the variety of the load history, not just“monotonic load”, we divide the hardening/softening rule into “isotropic” and “kinematic” parts. By assuming the isotropic part has a saturated limit, we conjecture if giving a lower limit of the force multiplier, the result of optimization will make sense in engineering: “Subjected to a varying load under the collapse load but above the lower limit, structures will be safe.”
Also, a simple algorithm is given: By classifying the internal work of trusses at first, we can uncouple two complementary trios. Therefore, the variables which need perturbation can be reduced and only nodal displacements remain. Then, we call the Optimization Toolbox of MATLAB to solve this unconstrained nonlinear programming problem. Moreover, five examples with an incremental method are given to verify this theory and method. The results show that the theory and algorithm are practicable for small and medium structures. They can also deal with local instability.
Subjects
極限分析
崩塌載重
軟化
非線性最佳化
limit analysis
collapse load
softening
nonlinear programming
Type
thesis
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