T-elements analysis of plated on unilateral elastic Winkler-type foundation
This paper presents a hybrid–Trefftz finite element algorithm designated as fictitious load approach. Its originality resides in the formulation and practical application of concepts which make it possible to account for the unilateral contact conditions of a plate without modification of the finite element mesh. To reach this aim, the approach allows the movable interface between the contact and non–contact parts of the plate to travers any finite element subdomain. The adjustments are confined to fictitious load dependent terms, while the element stiffness matrices remain unchanged during the whole iterative process. Several numerical examples are analysed to assess the effectivity of the T–element algorithm and to compare it with some of the existing solutions of the same problem.
Efficient analysis of plates on nonlinear foundations
Abstract This paper presents efficient analysis of plates on nonlinear foundations. The Reissner plate theory is used to model plates. Foundations are presented as the Winkler springs or the elastic half space. The developed analysis is mainly presented for tensionless foundation; however as demonstrated, it is straightforward extended to analysis of elastic-plastic foundations. The plate is analyzed using the boundary element method (BEM). Unlike the traditional BEM which uses equations in form ([H] {u} = [G] {t}), the presented formulation uses finite element like equations, in the form of ([K] {u} = {P}). An innovative formulation is presented to derive the relevant plate stiffness matrix [K] and load vector {P} from the BEM integral equation. Iterative procedures together with condensation process are used to eliminate degree of freedom at failed zones. Results of the present analysis are more accurate than those obtained from previously published results. The main advantages of the presented technique are its simplicity and accuracy and it gains both advantages of the boundary element and the finite element methods.
Parboiled rice effluent: A wastewater niche for microalgae and cyanobacteria with growth coupled to comprehensive remediation and phosphorus biofertilization
Abstract The potential of microalgae and cyanobacteria for bioremediation of wastewater by nutrient uptake combined with simultaneous biomass production is a well recognized perception of today's world. The present study illustrates the treatment of a highly polluted wastewater generated during parboiling of paddy in rice mill industries, widely operational in developing countries where rice is the staple food crop, with the help of microalgal and cyanobacterial isolates capable of growing at high rates in parboiled rice mill effluent (RME). This endeavor leads to comprehensive bioremediation of the said effluent and subsequent use of the harvested biomass as slow release phosphorus biofertilizers and the treated effluent for crop irrigation. The RME-acclimatized algal consortium demonstrated highest growth in terms of fresh weight and greatest remediation efficiency at the end of 36 days' treatment of RME, with 93.9% phosphorus and 100% ammonia-nitrogen removal, 98.7%, 91.6% and 93.5% reduction in biological oxygen demand, chemical oxygen demand and total dissolved solid, respectively, and an increment of 186 ± 0.3 mg L − 1 dissolved oxygen, bringing down the pollutants level well below the discharge limits suggested by Central Pollution Control Board, India. Additionally, microalgae in the consortium aggregated in clumps spontaneously in presence of the filaments of Phormidium sp. facilitating easy harvest. The RME-acclimatized algal consortium demonstrated highest accumulation of polyphosphate (poly-P) (0.76 ± 0.01% of dry weight) as well as highest release of phosphorus in non-sterile soil emphasizing the essential role of soil phosphorus solubilizing organisms to leach soluble phosphorus from the insoluble poly-P present in the biomass. The rice seedlings watered with treated RME also showed improved growth effect on shoot height and leaf width. The study results establish the suitability of RME as an excellent growth media for microalgae and cyanobacteria.