Abstract
The proposed detection algorithms are assigned for the hpq-adaptive finite element analysis of the solid mechanics problems affected by the locking phenomena. The algorithms are combined with the M- and hpq-adaptive finite element method, where M is the element model, h denotes the element size parameter, and p and q stand for the longitudinal and transverse approximation orders within an element. The applied adaptive scheme is extended with the additional step where the locking phenomena are a posteriori detected, assessed and resolved. The detection can be applied to shear, membrane, or shear–membrane locking phenomena. The removal of the undesired influence of the numerical locking on the problem solution is based on p-enrichment of the mesh. The detection algorithm is also enriched with the locking assessment algorithm which is capable of determination of the optimized value of p which is sufficient for the phenomena removal. The detection and assessment algorithms are based on a simple sensitivity analysis performed locally for the finite elements of the thin-walled domain. The sensitivity analysis lies in comparison of the element solutions corresponding to two values of the order p, namely current and potentially eliminating the locking. The local solutions are obtained from the element residual method. The elaborated algorithms are original, relatively simple, extremely reliable, and highly effective.
Highlights
This paper concerns application of the algorithms for detection, assessment and resolution of numerical locking in the hpq-adaptive finite element elastic analysis of thin-walled structures or complex structures which include thin-walled, solid, and transition parts
As results of the analysis, we present the meshes corresponding to three performed courses of adaptation: standard hp-adaptation and such adaptations preceded by the modification of the initial mesh with the increased longitudinal order of approximation p, equal either to the maximum or optimized value
The first one corresponds to the standard hp-adaptivity composed of the h- and p-adaptation steps only
Summary
This paper concerns application of the algorithms for detection, assessment and resolution of numerical locking in the hpq-adaptive finite element elastic analysis of thin-walled structures or complex structures which include thin-walled, solid, and transition parts. We focus on the theoretical and methodological aspects such as the idea and justification of the elaborated algorithms for a posteriori detection and assessment of the phenomenon. The necessary modification of the applied hpq-adaptive algorithms is of our interest. The paper presents application of the introduced detection, assessment, and resolution algorithms in the hpq-adaptive analysis of structural elements. These algorithms are investigated in the contexts of their generality, reliability, and effectiveness
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