Plastic Solutions Research Articles

Information-Based Plastic Material Tracking for Circular Economy—A Review

At the moment, it looks like the plastics recycling industry is skimming only low-hanging fruits of its business. To reach intended targets, a greater effort and disruptive innovations are necessary. Physical- or digital-information-based solutions for tracking plastic material can support the circular economy and help to overcome hurdles along the value chain. In this paper, the scientific literature and initiatives in four different technology areas for information-based tracking solutions are reviewed and analyzed. Physical markers can improve sorting efficiencies on short notice but adhere some technical difficulties. Blockchain as a new concept promises high transparency and security, with the drawbacks of energy-intense verification and technical uncertainties. As a third group, the digital product passport claims a combination of physical and digital solutions with open questions on data ownership. The fourth and last group includes standards and certification systems that aim for maximum consensus with slow market implementation. To enable an integrated circular economy of plastics, plastic material tracking solutions must experience broad acceptance by all players along the value chain in the plastics industry and they should additionally be supported by society.

Plastic Displacement Solutions for Two-Way Unequal-Pressure Non-Circular Tunnels Based on Mogi–Coulomb Criterion and Applications

Plastic Displacement Solutions for Two-Way Unequal-Pressure Non-Circular Tunnels Based on Mogi–Coulomb Criterion and Applications

Pedagogical conditions for the formation of creative independence of art and pedagogical university students in China and Russia: comparative analysis

Creative independence of art students is one of the most important conditions for successful study and further employment in modern art education in the Russian Federation and the People's Republic of China. The purpose of this publication is to identify those organizational-pedagogical, psychological-pedagogical and didactic conditions in modern Russian and Chinese art universities that activate the creative independence of students. In Russia, they are more focused on stimulating the ability of students to perform educational activities independently of teachers. In China, the main focus is on independence in the creative search of students. The analysis shows that the formation of creative independence in the educational process in pedagogical universities of Russia and China in the conditions of personality-oriented learning allows students to improve both visual abilities and skills of a future teacher-artist through complexes of creative tasks or projects and participation in exhibition projects. The preparation of curricula with an emphasis on the independent work of students is a priority direction of development in such educational institutions, which is focused on the creative and research activities of students, but within the framework of certain educational tasks. The latter do not restrict the freedom of students, but, on the contrary, are those "difficulties" that provoke independence in plastic and meaningful solutions in creative works.

Evaluating friction angles for clays: piezocone tests compared with Atterberg limits

A limit plasticity solution for evaluating the effective stress friction angle in clays from piezocone tests was assessed and compared with the popular notion of using laboratory Atterberg limits on remoulded specimens. The results showed that the in situ piezocone-based method provided a far more accurate and robust interpretation of the friction angle values of 155 separate clays than empirical correlations with plasticity index when compared with laboratory benchmark values obtained from triaxial compression tests. For illustration, the piezocone-based method was shown successfully to capture the effective stress parameter of four clays with friction angles of 20–37°: normally consolidated kaolin clay in chamber tests; natural soft clay deposit located at Bothkennar, UK; Troll offshore clay in the North Sea; and soft plastic lacustrine deposits in Bogota, Colombia.

Succinic Acid Production from Oil Palm Biomass: A Prospective Plastic Pollution Solution

Plastic pollution has placed a significant emphasis on the need for synthesising bioplastics, such as polybutylene succinate (PBS), which is derived from succinic acid. Furthermore, environmental concerns and the depletion of non-renewable fossil fuels have initiated an interest in exploring the biotechnological route of succinic acid production via fermentation. Consequently, oil palm biomass might be a prospective substitute for the costlier pure carbon source, which is more sustainable and cost-effective due to its abundance and high lignocellulosic content. The current review focuses on the potential of oil palm biomass utilisation to synthesise succinic acid and its associated bioplastics. The pretreatment and hydrolysis of various oil palm biomass and studies on bioplastics generation from oil palm biomass are also discussed. This review also identified the challenges of manufacturing succinic acid from oil palm biomass and included several recommendations.

The specifics of the choreographic interpretation of the main characters in the ballet "Zephyr and Flora, or Metamorphoses" (2021) in the context of modern plastic trends.

In this article, an attempt is made to comprehend the features of the choreographic embodiment of the images of the main characters (Zephyr and Flora) by choreographer A.S. Belyakov in the play "Zephyr and Flora, or Metamorphoses" (2021). This ballet is a modern appeal to the theme of the pre–romantic ballet Sh. Didlo (early XIX century). Such a plan cannot but be relevant, as well as the study of its creative results, first carried out in this article. Based on the methods of ballet studies analysis approved by Russian historians and ballet theorists (Dobrovolskaya, Krasovskaya, Slonimsky, Surits), the author applied comparative historical, ideological, artistic and analytical methods, as well as the method of included observation (based on personal experience working on the part of Flora). The main research tools were analytical description and semantic analysis of the variation of Zephyr and the duet of Zephyr and Flora. With their help, we managed to draw the following conclusions. The choreographic vocabulary of the fragments is distinguished by an organic combination of classical positions and pas with the author's movements (pictorial, ornamental poses; somewhat broken positions of the arms and body; originally modified technical elements). The dramaturgy of the modern reading of the plot of the pre-romantic ballet is developed by the choreographer by plastic (not pantomime) means in key dance fragments. Thus, the choreographic embodiment of the images of Zephyr and Flora demonstrates an organic synthesis of the ideological idea and the general aesthetics of pre-romantic ballet with the unconventionality and innovation of the modern author's plastic solution.

Plastic waste management in the smart cities: Poland and Turkey as a case study

Introduction/background: Waste in various forms, such as solid waste, gaseous waste, and liquid waste, increases as a result of population growth, urbanization, and industrialization, and has a global impact. Waste management entails activities such as reuse, recycling, and reducing waste generation, as well as other strategies to combat the effect of waste generation caused by increasing population and industrialization. Monitoring is a critical function of waste management because it is required to address waste management issues such as waste generation, waste collection, waste transportation, waste treatment, and waste disposal. The article presents plastic waste management in the context of smart cities. Purpose: The goal of the article is to present and compare of the production of plastic waste in Poland and Turkey in the context of smart cities. Sustainable and eco-innovation plastic waste management solutions to reduce plastic waste are provided to be implemented in smart cities. In this study, smart cities are explained, how to manage plastic waste by using smart city components, and methods of dealing with plastic waste are explained. Methodology: The article is based on a review of the literature, own observations and own experience. The currently available plastic waste management solutions were analyzed and examples in the implementation of the technology in a smart city are described. Findings: The incorporation of smart city technology into waste management practices provides a smart way to solve waste issues. The main of plastic waste management is to develop methods to transform plastic waste into a circular economy. As estimated by 2030 plastic leakage to ecosystems should be 30% reduced, double the global recovery of plastic (collection and recycling), and shift to sustainable inputs for remaining plastic, including recycled content, sustainably sourced biocontent, advanced products and reducing unnecessary plastic through a business model, innovation, reduction and substitution. Originality: The goal of waste management is to recover as much useful material as possible, including energy. Waste generated in smart cities is a category of municipal waste. Traditional approaches to waste management have failed because they are not reliable or sustainable because they require a lot of input for little or no work output. The incorporation of smart city technology into waste management practices provides a smart way to solve waste issues. The main of plastic waste management is to develop methods to transform plastic waste into a circular economy. Keywords: Plastic wastes, waste management, smart cities, eco-innovation solutions.

Influence of Scenography Development on Artistic Interpretation in Plastic Directing

The purpose of the article is to reveal the specifics of the development of scenography in plastic directing and its influence on artistic interpretation in the context of the peculiarities of theoretical developments and practical implementation in stage practice of leading theatre directors of the 20th – early 21st centuries. Research methodology. The research is based on modern art history and philosophical concepts of the study of the phenomenon of development of unique forms and the principles of the artistic relationship between direction and scenography. Taking into account the interdisciplinary nature of the issue, the cultural-historical method has been applied in research and analysis of the pictorial-plastic solution of the performance (to define the concept of "plastic stage forms" and "plastic drawing of acting" in the context of cultural, art history and philosophical concepts). The method of comparative analysis has been applied to combine methods and ways of representing scenography in theoretical works and practical activity of leading theatre directors. The typological method has been used to identify the factors of formation of the performance plastic solution. Scientific novelty. An art-historical study of the stage space approximation to the forms of the human body in the context of the specifics of theatrical art is carried out. The process of the transition of scenographic design from detached to dynamic in the context of transformational processes of theatrical art is considered. Common and different values, as well as forms of scenography representation in the theoretical works and practical activities of leading theatre directors of the 20th – early 21st centuries, are identified and analysed. Conclusions. The issue of artistic space in the organisation of the temporal component of the stage production plays an extremely important role in plastic directing, namely the circumstances that determined the specificity of the spatial structure of the literary original source or the director's interpretation and, accordingly, have an impact on its artistic and figurative interpretation. In the Ukrainian theatrical art, the relationship between directing and scenography is expressed as a sole management of all means of scenic expressiveness, namely plastic directing, which is based on the plastic unity of the stage work. The uniqueness of the scenography of the leading Ukrainian directors’ productions of the late 20th and early 21st centuries manifests itself in the artistic interpretation of the selected literary material and the innovative detection of the semantic and content saturation of their formal and plastic solution. Key words: scenography, stage form, plastic, theatre art, theatre artist, scenery, scenographic decoration

Stress distribution model for the entire plastic zone of conical indentation with power-law hardening materials

<p indent="0mm">The classical contact mechanics provides an elastic conical indentation solution, and verifies that the strain field of elastic-plastic indentation with an arbitrary blunt indenter mostly satisfies the expanding cavity model. This study reviews the stress solution of the elastic zone for conical indentation using power-law hardening materials derived from predecessors based on the expanding cavity model and elastic-plastic mechanics. Furthermore, the expression of von-Mises equivalent stress in the plastic zone of conical indentation is determined according to the plastic stress solution of an internally pressurized thick spherical shell. The numerical verification revealed that the calculated equivalent stresses via finite element analysis are consistent with the theoretical solution of the elastic zone for conical indentation. However, a clear deviation in the entire plastic zone for the power-law hardening materials is still observed. Furthermore, to accurately describe the equivalent stress in the entire plastic zone of conical indentation for power-law hardening materials, a novel model for the indented stress distribution is established by combining the dimensional analysis method and finite element simulation. Finally, the stress model was verified using a wide range of ductile materials. The comparison results revealed that all of the calculated equivalent stresses are consistent with the model predictions for the entire plastic zone.

Investigating the mechanism of splitting failure in deep high sidewall cavern based on complex function and strain gradient

Owing to excavation-induced unloading, high sidewalls of underground powerhouse are often subjected to splitting failure, which produces many adverse effects to the construction of the cavern. To reveal the formation mechanism of splitting failure, we proposed a novel elastic–plastic damage softening model based on the strain gradient theory and the elastic–plastic damage theory. Using the ODE45 program in MATLAB, the numerical solution of the displacement and stress of circular cavern was solved based on the newly proposed elastoplastic damage model. We then adopted the complex function method and used the Schwarz-Christoffel integral formula to obtain the mapping function from the outer domain of high sidewall cavern to the outer domain of the unit circle. Finally, the elastic–plastic region and the displacement distribution of high sidewall cavern were obtained by mapping the obtained elastic–plastic solution of the circular cavern under the axisymmetric condition. The numerical analysis results were consistent with the previous geomechanical model test results. The results presented that the stress of high sidewall of an underground powerhouse exhibits an oscillating variation with alternating peaks and troughs, which is the mechanical mechanism of splitting failure.

Experimental, numerical and analytical study to develop a design method for bending and shear resistances of 3D printed beetle elytron inspired sandwich plate (beetle elytron plate)

Beetle elytron plate (BEP) is a new type of sandwich structure inspired by the internal architecture of beetle elytra and characterized by trabeculae in the core to achieve better mechanical resistance compared to conventional honeycomb sandwich plate under lateral loads. To take advantage of this improved performance in design, this paper presents, for the first time, a series of static four-point bending and shear tests for buckling and post-buckling behaviour of small-scale 3D printed BEPs until failure. Tensile coupon tests were also carried out on the 3D printed material. The experimental results are then used to validate ABAQUS numerical modelling that previously could only be partially carried out due to a lack of experimental data. The test results confirm large increases in BEP resistances compared to conventional honeycomb sandwich plates of the same dimensions. The observed BEP failure mode under bending is post-buckling of the compressive skin. Assuming that the post-buckling stress of BEP can be calculated in the same way as conventional sandwich plate, and making use of the elastic–plastic buckling stress solution for BEP that had previously been proposed by the authors, this paper proposes a simple method to calculate the post-buckling stress of BEP for design purpose. For shear resistance, the shear buckling stress of the trabecular core of BEP can be calculated in the same way as for conventional honeycomb sandwich plate except for using the web width between the near edges of the two adjacent trabeculae. The proposed calculation methods give results in good agreement with experimental results, with the maximum difference being 8%. The difference would be even lower if the smooth 3D printed surface is under compression.

Undrained trapdoor and tunnel face stability revisited

In this study, closed-form solutions are presented for two classical problems: the load exerted on strip or circular trapdoors and the stability of tunnel headings in purely cohesive soils, considering both the case of a constant undrained shear strength and of a linear vertical strength profile. The solutions are based on a minor modification of Gunn's lower-bound plasticity solution. According to comparative numerical stress analyses and finite-element limit analyses, the proposed equations accurately estimate trapdoor loads and face support pressures in soils with uniform strength, while they are slightly conservative in the case of depth-dependent shear strength. Thus, they are appropriate for the assessment of the stability of underground structures in saturated, low-permeability soils subjected to short-term loading and exhibiting depth-dependent strength – which, so far, has only been possible numerically.

Aggregation kinetics of polystyrene nanoplastics in gastric environments: Effects of plastic properties, solution conditions, and gastric constituents

Nanoplastics are inevitably ingested into human gastric environment, wherein their aggregation kinetics and interactions with gastric constituents remain unclear. This study investigated the early-stage (20 min) and long-term (1–6 h) aggregation kinetics of four commonly-found polystyrene nanoplastics (PSNPs) including NP100 (100-nm), A-NP100 (100-nm, amino-modified), C-NP100 (100-nm, carboxyl-modified), and NP500 (500-nm) under gastric conditions. Five simulated human gastric fluids (SGFs) including SGF1-3 (0–3.2 g/L pepsin and 34.2 mM NaCl), SGF4 (400 mM glycine), and SGF5 (nine constituents), three pH (2, fasted state; 3.5, late-fed state; and 5, early-fed state), and 1–100 mg/L PSNPs were examined. Aggregation rates ranked NP100 > A-NP100 ≈ C-NP100 > NP500, SGF5 > SGF4 > SGF3 > SGF2 > SGF1, and pH 2 > 3.5 > 5. Increasing PSNP concentration enhanced aggregation rate up to 13.82 nm/s. Aggregation behavior generally followed the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Pepsin, glycine, and proteose-peptone strongly influenced PSNP stability via electrostatic interaction and steric hindrance imparted by protein corona. Freundlich isotherm suggested that PSNPs adsorbed organic constituents following lysozyme > porcine bile > proteose-peptone > pepsin > glycine > D-glucose, inducing changes in constituent structure and PSNP properties. These findings provide insights on the transport of nanoplastics in the gastric environments.

An exact solution of active earth pressures based on a statically admissible stress field

Static lateral earth pressure problems are a central and long-standing topic in geotechnical engineering, but their exact solutions are lacking. This study is dedicated to providing an exact solution for active earth pressure exerted against rigid retaining walls with various wall geometries, backfill geometries, and wall roughness. A numerical model based on the rigid plastic analysis, namely a fully plastic solution, has been successfully developed to search out statically admissible stress fields in the backfills. In particular, Sokolovski’s theory coupled with the Mohr-Coulomb criterion has been adopted to enable the statically admissible stress fields to be developed. Robust numerical frameworks based on the fifth-order adaptive Runge-Kutta method, and a shooting technique has demonstrated efficacy in coping with the stress singularity that appeared in the analyzed domain, thus the admissible stress fields have been successfully figured out. The accuracy of the proposed solution is satisfactorily verified and validated by comparing the obtained results with exact values and those of experimental results available in the literature. The admissible stress fields explored in the backfills of rigid walls elucidate the load transfer mechanism of cohesionless materials in the backfills; the potential effects of various parameters e.g., wall geometries, backfill geometries, and wall roughness on the active earth pressure coefficients have been disclosed thereof. In essence, this study provided a conservative answer for the static active earth pressure problems whereby the exact values of active earth pressure coefficients are tabulated and provided for engineering practice.

Review of Selected Issues in Anisotropic Plasticity under Axial Symmetry

The present review paper consists of two main parts, which are not connected. The first part is devoted to a general axisymmetric elastic–plastic plane stress solution, assuming polar anisotropy. Strains are infinitesimal. The principal stress trajectories coincide with the principal axes of anisotropy. No restrictions are imposed on the yield criterion other than the conventional restrictions imposed on the yield criteria in plasticity. The plastic portion of the strain rate tensor is determined from the associated flow rule. A simple example illustrates the general solution. The second part is devoted to the stationary ideal flow theory for anisotropic materials under axial symmetry. The elastic portion of the strain tensor is neglected. A piece-wise linear yield criterion is adopted. This criterion generalizes Tresca’s yield criterion. The existence of ideal flow is proven. It is also shown that the available solutions for Tresca’s yield criterion can be used for deriving solutions for the yield criterion under consideration. Miscellaneous topics are shortly discussed in the third part of the paper.

ASSESSMENT AND ANALYSIS OF IMPROVEMENT ELEMENTS OF THE VNAU PARK ZONE

The article presents the results of research, evaluation and analysis of elements of landscaping of Vinnytsia National Agrarian University. The university complex is one of the main elements of the urban environment, which requires a special attitude and place in the planning and organizational structure of the city. The environment should provide students and teachers with optimal conditions for fruitful educational and scientific activities and a variety of recreation, sports. It has been established that the territory of the university has a clear combination of buildings connected by passages into a system that provides opportunities for a harmonious combination of buildings and greenery. The proportions of individual groups of buildings, their plastic solution and spatial development in the depth of the site, the combination of open and closed spaces, extensive use of green courtyards and small architectural forms give unity and beauty to the architectural ensemble of higher education. It is investigated that pedestrian traffic is correctly organized during the design of the complex. The central esplanade is located and arranged in such a way that it connects all the zones and ensures their interconnection and at the same time is a place for students to communicate. It is estimated that alleys and paths in the park zone of VNAU occupy about 20% of its area. Forced curves are used to create a variety of accents, such as trees and shrub groups. There are 5 classes of roads, paths and sites on the territory of the university, the condition of which is excellent. According to the analysis of landscaping elements, there are 34 benches for long-term rest and 14 benches for short-term rest near the university buildings. All presented benches are stationary and made of concrete, wood and brick. This number of benches is sufficient to ensure comfortable living conditions for students in all corners of the university. The benches are easy to use, their shape is simple, and the color organically fits into the overall color scheme of the territory.

Cytotoxicity and Genotoxicity of Polystyrene Micro- and Nanoplastics with Different Size and Surface Modification in A549 Cells.

BackgroundMicro- and nano-sized plastics (MPs and NPs) have become an environmental issue of global concern due to their small size, strong bio-permeability and high specific surface area. However, few studies have assessed the effect of polystyrene MPs and NPs on human lung cells. In this research, we evaluated the cytotoxicity and genotoxicity of polystyrene (PS) MPs and NPs with different sizes (2 μm and 80 nm) and surface modification (carboxy and amino functionalized polystyrene, pristine polystyrene) in A549 cells.MethodsThe zeta potential and hydrodynamic particle size of five types of PS plastic solutions were measured by dynamic light scattering, and their morphology and degree of aggregation were observed by scanning electron microscopy. After incubation of the PS plastics with A549 cells, the uptake and toxicity of the cells were assessed by fluorescence microscopy, laser scanning confocal microscopy, flow cytometry, MTT, micronucleus formation assay, and reactive oxygen species.ResultsThe cytotoxicity and genotoxicity of A549 cells caused by nano-level PS is more serious than that of micro-level. Compared with unmodified PS-NPs, more surface-functionalized PS-NPs were found inside the cells, especially the accumulation of PS-NH2. Cell viability and the induction of micronuclei (MN) are appreciably impacted in a dose-dependent way. Compared with pristine PS-NPs, functionalized PS-NPs showed stronger cell viability inhibitory ability, and induced more MN scores.ConclusionThis study shows that the intrinsic size properties and surface modification of PS plastics, the interaction between PS plastics and the receiving medium, intracellular accumulation are critical factors for evaluating the toxicological influences of PS plastics on humans.

Effect of Additional Cellulose Bacterial from Nata De Soya and Chitosan in Bioplastic Manufacturing

Plastics are synthetic polymers from petroleum or petrochemicals that are difficult to biodegrade by bacteria and microbes. Non-biodegradable plastics cause the accumulation of large amounts of plastic waste Solutions that can reduce plastic waste by making plastics that are easily biodegradable. In this study, tofu liquid waste is used as a basic material for the manufacture of bioplastics. Tofu liquid waste is waste generated from tofu production. This study aims to determine the effect of adding bacterial cellulose and chitosan on the manufacture of bioplastics from liquid waste tofu (whey) in terms of tensile strength, elongation, water solubility, and functional groups (FTIR) in accordance with PET plastic standards (Polyethylene terephthalate). The research procedure on the effect of adding bacterial cellulose and chitosan on the bioplastic fabrication of Nata De Soya. First, from tofu liquid waste, Acetobacter Xylinum starter was added and then fermented for 10-12 days to become Nata De Soya. After that it was neutralized with aquadest, removed the water by pressing, and dried to become bacterial cellulose. The process of making bioplastic with the addition of chitosan (grams) 2,3; 3.1; 3.9; 4.7 and 5.5 and bacterial cellulose (grams) 0.5 ;1.5; 3.9; 7; and 11. In the manufacture of bioplastics with the addition of Bacterial Cellulose and chitosan, it is appropriate, namely the tensile strength obtained will increase and the solubility in water decreases. From the results of our research, the best results were obtained in the addition of S5K5 with a tensile strength value of 9.665 MPa, an elongation value of 31.3%, and a solubility value in water of 17.9%. It has a higher tensile strength, smaller elongation and lower water solubility. The effect of the addition of chitosan on the tensile strength value can increase the tensile strength (Tensile Strength Value), the addition of bacterial bacterial cellulose and chitosan can affect the elongation of bioplastics getting smaller and the effect of chitosan can reduce solubility in water. It is good but still far from the standard PET (Polyethylene Terefelat) which is 60-80 Mpa.

Stage design as a directing decision tool

The aim of the article is to identify the features of stage design as a tool for representing the director's vision of the play in historical retrospect and at the present stage. Research methodology. The system method was used (for the study of scenographic design as a holistic and developed system); functional-typological method (to clarify the functions of stage design in the context of the specifics of design and directing); historical and cultural method (to consider this issue in the development of stage design), etc. Scientific novelty. Stage design as a unique tool for representing the director's vision of production is studied; the peculiarities of the conceptual and material sequence of the process of creating a visual image of the play are analyzed (according to D. Payne); the influence of the New Stagecraft movement on the formation of the modern concept of stage design was revealed; the specifics of stage design in traditional and non-traditional space are considered. Conclusions. Over the centuries, the artistic solution of stage production has undergone many different transformations, according to a specific period of historical development of theatrical art, recreating the environment in detail, minimizing to virtually free of scenery and props stage space, representing innovative technologies and others. At the present stage, theatrical art in general and directing in particular, continues the search for a new form of production. Under the influence of intensification of integration processes, which technologically and informationally combine various means of communication and information, as well as in accordance with the development of a specific culture of creating and showing theatrical performances, an important part of stage design of the XXI century. became audiovisual media - television, cinema, video and multimedia. The study found that in the process of historical development of the theater, the focus of the set designer has shifted from the interpretation of the text on a given stage space to the deconstruction of the found space in a critical context. However, stage design remains a powerful expressive force in the work of the playwright and director, strengthening them as a visual imprint, organically integrated into the semantic universe of the play. The stage design of a theatrical performance is the result of logical, figurative thinking and intuitive feeling expressed through an idea or a central theme. The original organization of space, drama, functionality of scenery and costumes, multimedia, lighting solution embody in a plastic solution the idea of ​​the play, staged by the director. Remaining the most important figure in the theater, the director finds visual support in the scenographic rhetoric of forms, volumes and chromatics in the process of creating an ideal sphere, with a single homogeneous content. Key words: stage design, artist, director, performance, visual-symbolic interpretation, scenery.

Ideal Flow Design of Plane-Strain Bending Driven by Springback

The present paper is concerned with the design of the plane-strain bending of wide sheets driven by the sheet’s geometric shape after unloading. The solution is based on the ideal flow theory. It determines the loading path (the dependence between the dimensionless bending moment and the dimensionless tensile force) that produces the desirable shape. The ideal flow theory is valid for the rigid perfectly plastic material model. A method proposed in the literature combines a rigid plastic solution at loading and an elastic solution for springback. The final design solution is practically analytical. A numerical method is only necessary to solve a system of transcendental equations. An illustrative example is provided. This example shows that, in some cases, it is sufficient to use the solution at loading to determine an accurate loading path that produces the desirable sheet’s shape after springback.