A numerical shakedown analysis method for strength evaluation coupling with kinematical hardening based on two surface model

et al. 2021

Preprint

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Structural optimal design is traditionally performed according to the elastic limit rule which makes the structure overweighted or strength over conservative to an extent. Shakedown theory is implemented in the present study in order to measure load-capacity performance of structure. It can determine the strength of a structure under arbitrary varying loads without loading history where failure form of incremental collapse, ratcheting and alternate plasticity will be avoided. The current research subsequently provides a parameter optimal design scheme with respect to maximum structure strength and strength-to-weight performance in the framework of shakedown which makes the optimal structure design in a relatively practical way. With this motivation, the formula of proposed shakedown limited parameter optimization problem is derived and solved based on genetic-gradient coupling algorithm. The present coupling algorithm is essentially solve a double-loop problem where the inner loop adopt interior point method to solve shakedown problem under a given parameter combination while the outer loop use genetic algorithm to find the optimal parameters based on a given shakedown fitness. In addition, external database technique is applied to accelerate computation and prevent unexpected interrupt. Subsequently, a test example which is a optimal parameter design problem of plate with a circular hole is presented to demonstrate the accuracy and effectiveness of the proposed method and algorithm. In addition, the proposed method is also utilized to determine the optimal load-bearing capacity of a airtight module to be used in a manned spacecraft. Moreover, optimal shakedown load design results of the manned airtight module as well as optimal strength-to-weight efficiency design results are given in the end. This study confirmed that genetic-gradient coupling algorithm is a effective means for determine the optimal parameter in accordance to the shakedown load domain.

Section: Test Example Of the Proposed Work Flowsupporting

confidence: 89%

Section: Low Bound Limit and Shakedown Theorem For Elastic-perfectly Plastic Materialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Shakedown strength based parameter optimization technique and its application on designing an airtight module

Huang

et al. 2021

Preprint

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“…Abdalla and Megahed (2018) used the nonlinear superposition method to calculate the elastic shakedown limit loads of spherical vessels with radial and oblique nozzles based on Melan's lower bound shakedown theorem and then compared with the experimental test results. Huang et al (2019) developed a numerical method for extended shakedown analysis based on a two surface plasticity model of kinematic hardening. Zhuang et al (2019) developed a 3D analytical shakedown solution in railway structure under multiple Hertz loads.…”

Section: Introductionmentioning

confidence: 99%

A numerical method of lower bound dynamic shakedown analysis for 3D structures

Peng

Tang³

et al. 2021

Purpose The safety assessment of engineering structures under repeated variable dynamic loads such as seismic and wind loads can be considered as a dynamic shakedown problem. This paper aims to extend the stress compensation method (SCM) to perform lower bound dynamic shakedown analysis of engineering structures and a double-closed-loop iterative algorithm is proposed to solve the shakedown load. Design/methodology/approach The construction of the dynamic load vertexes is carried out to represent the loading domain of a structure under both dynamic and quasi-static load. The SCM is extended to perform lower bound dynamic shakedown analysis of engineering structures, which constructs the self-equilibrium stress field by a series of direct iteration computations. The self-equilibrium stress field is not only related to the amplitude of the repeated variable load but also related to its frequency. A novel double-closed-loop iterative algorithm is presented to calculate the dynamic shakedown load multiplier. The inner-loop iteration is to construct the self-equilibrated residual stress field based on the certain shakedown load multiplier. The outer-loop iteration is to update the dynamic shakedown load multiplier. With different combinations of dynamic load vertexes, a dynamic shakedown load domain could be obtained. Findings Three-dimensional examples are presented to verify the applicability and accuracy of the SCM in dynamic shakedown analysis. The example of cantilever beam under harmonic dynamic load with different frequency shows the validity of the dynamic load vertex construction method. The shakedown domain of the elbow structure varies with the frequency under the dynamic approach. When the frequency is around the resonance frequency of the structure, the area of shakedown domain would be significantly reduced. Research limitations/implications In this study, the dynamical response of structure is treated as perfect elastoplastic. The current analysis does not account for effects such as large deformation, stochastic external load and nonlinear vibration conditions which will inevitably be encountered and affect the load capacity. Originality/value This study provides a direct method for the dynamical shakedown analysis of engineering structures under repeated variable dynamic load.

“…Composites of multiple phases were studied by homogenization theory [22,23], and non-periodic random composites, auto modeling techniques, and statistical measures [24][25][26] were involved. Different hardening models of material were analyzed [25][26][27][28][29][30][31][32], as were temperature loads [28,29] and multidimensional load domains [6,30]. In the macro scale, besides pressure vessels and piping, components of high-speed train were also studied [31,32].…”

Section: Introductionmentioning

confidence: 99%

Lower bound limit and shakedown analysis of orthotropic material

Fang

Mathematics and Mechanics of Solids

Chen

et al. 2020

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We present in this study a new approach for predicting the plastic and shakedown limits of structures composed of orthotropic materials. In this approach, the Hill yield criterion is introduced to Melan’s theorem. By formulating the problem by means of the finite element method and solving the resulting large-scale nonlinear optimization problem we successfully predict the plastic and shakedown limits of structures having complex geometries made from multi-orthotropic materials. Several numerical examples are elaborated in this study for evaluating the accuracy, general applicability, as well as the efficiency of the established numerical scheme. Overall, the study confirms that the direct method can be extended and adopted as a viable means for design and analysis of structures made of orthotropic materials.