Principle Of Minimal Potential Energy Research Articles

Computer simulation for parametric study of concrete system: Introducing novel reinforcement for concrete construction materials

Concrete is a primary construction material in the building industry. Formwork is crucial in facilitating the implementation of geometric designs and enhancing the structural integrity of concrete components. Additionally, it represents a significant expense in the building of concrete structures. The use of formwork has a lengthy historical background, with several formwork systems being employed in various projects. When designing and choosing a formwork system, it is important to consider many needs, including safety, cost, structural geometry, construction time, and surface quality. This article introduces a computer simulation for conducting a parametric analysis of concrete systems using a new reinforcing method for concrete building materials. To achieve this objective, the current relevant concrete material is simulated using higher-order shear deformation theory, the minimal potential energy principle, and an analytical solver. Halpin–Tsai homogenization technique and the role of the mixture are used to predict the mechanical properties of the presented innovative reinforcement. The mathematical formulation of a Haber–Schaim foundation constructed from auxetic material inside the Cartesian coordinate system is expressed. The results show that in the highest velocity, the influence of the graphene oxide powders (GOP) distribution pattern on the acceleration of the system than other values of velocity. Also, as an applicable suggestion, by a less change in the amplitude of the structure with higher values of GOP weight fraction, the velocity of the structure changes drastically, While, this trend for lower values of GOP weight fraction has a noticeable change. Finally, some suggestions for improving the dynamic stability of this kind of innovative concrete structure will be given in the results section for civil and mechanical engineers.

Quasistatic inflation processes within compliant tubes

In former work , , and , a mechanical system was considered that models a segment of a live or artificial worm or a balloon for angioplasty that is placed within a cylindrical rigid or compliant tube (vein). Based on the Principle of Minimal Potential Energy and treated as an optimal control problem with state constraint the authors derived a system of differential equations that describes the statics of the inflation process including the shape of the inflated system and the contact forces between balloon and vein. This paper now presents corresponding simulation results. A short but complete introduction to the theory makes the paper selfconsistent.

Parametric Studies of Shape Memory Alloy Hybrid Composite Laminates Under Low-Velocity Impact

AbstractIn the paper, the influence of shape memory alloy (SMA) by varying the parameters such as volume fraction, orientation, and temperature on the hybrid-SMA composite laminate subjected to low-velocity impact is studied. A theoretical model for the composite laminated plate bonded with SMA reinforced layers is presented. The constitutive relation of the SMA layer is obtained by using the method of micromechanics. The governing relations obtained can be used for theoretical predications of thermomechanical properties of SMA plies in this paper. The analytical expressions for the hybrid SMA composite plate are derived based on Tanaka's constitutive equation and linear phase transformation kinetics presented by Liang and Rogers.The laminated plate theory, first-order shear deformation theory and minimal potential energy principle is utilized to solve the governing equations of the hybrid composite plate and calculate the absorbed energies including tensile, shear and bending.An orthogonal array and analysis of variance is employed to investigate the influence of the mentioned parameters on the energy absorption of the hybrid laminated plate. The results showed that the effects of the phase transformation temperature are more significant than the effects of the volume fraction and orientation of SMA on structural energy absorption.

Analysis of Shape Memory Alloy Hybrid Composite Plates under Low Velocity Impact

This paper presents the analysis of smart hybrid composite plate with embedded shape memory alloy (SMA) wires subjected to low-velocity impact. The SMA wires were embedded within the layers of the composite laminates and the numerical calculation was used in the impact analyses of the laminated hybrid composite plate. The laminated plate theory, first-order shear deformation theory and minimal potential energy principle was utilized to solve the governing equations of the hybrid composite plate analytically. Energy absorption of hybrid composites can be successfully analyzed using analysis of variance (ANOVA). The results indicated that temperature effect is significant during the transition phase and SMA can effectively improve impact-resistance of the hybrid composite laminated plate. In addition, this hybrid structure is an advanced design concepts that can strengthen the impact resistance capability and enhance the carrying loading efficiency of the structure.

Analytical and finite element modelling of long plate mode jumping behaviour

Trapezoidal sheeting of thin-walled steel is applied frequently for roofing and cladding. As such, it is loaded by a concentrated load (at the support) and a bending moment. A recently developed model to predict the sheeting's failure behaviour leaves the question open whether mode jumping (the phenomenon where a plate dynamically changes its buckling mode during an increasing load) should be taken into account in the model. This article presents the analytical and finite element modelling of square and long plates, which, depending on the boundary conditions, may represent the compressed flange of trapezoidal sheeting. The analytical modelling is based on the combination of several displacement functions and using the principle of minimal potential energy. Hereafter the stability of each part of the resulting equilibrium curves is determined. A spin-off of the analytical model is an analytical expression for a current curve-fitted based prediction formula for the post/pre-buckling stiffness ratio by Rhodes. Furthermore, the accuracy range of a solution by Williams and Walker for the far-post buckling behaviour can be confirmed. The finite element modelling has been carried out by implicit dynamic, and explicit (dynamic) simulations. Both for the load levels and the buckling mode sequences, the analytical and finite element models give equivalent results. It is concluded that for the specific boundary conditions that represent the situation of a compressed flange for trapezoidal sheeting, it is very likely that mode jumping will not occur.

Nonlinear Responses of Nanoscale FGM Films Including the Effects of Surface Energies

A nonclassical thin plate theory is developed for the nonlinear elastic behavior of functionally graded films of nanoscaled thickness. The film bulk is modeled using the classical continuum theory of elasticity associated with the Kirchhoff hypothesis and the nonlinear strain of von Karman type. The elastic deformation of surface layers is modeled by the theory of surface elasticity proposed by Gurtin and Murdoch. The governing differential equations and boundary conditions including surface effects are derived based on the principle of minimal potential energy. A functionally graded material strip made of aluminum and silicon, whose effective bulk material properties are predicted using the Mori-Tanaka model with a power-law volume fraction profile, is considered as an illustrative example of application of the present model. It is shown that the size-dependent nonlinear responses vary with the aspect ratio and the volume fraction profile of the constituent material phases.

Geometrically nonlinear analysis of hyperelastic solids by high-order tetrahedral finite elements

The purpose of this study is to develop a computer code for accurate prediction of the mechanical behavior of hyperelastic solids under large deformation and finite strains. It is used, in the present work, the Lagrangian positional version of the Finite Element Method, in which the degrees of freedom are current positions instead of displacements. The main mechanical variables are the Green-Lagrange strain and the second Piola-Kirchhoff stress tensors. Isoparametric tetrahedral solid finite element of any approximation degree is employed with full integration in order to obtain accuracy. In order to be general, it is developed a numerical strategy to determine the shape functions coefficients of any order, following tetrahedral basis. The solid equilibrium is achieved at the current position by means of the Minimal Potential Energy Principle regarding positions and is solved by the Newton-Raphson iterative scheme. It is important to mention that the adopted constitutive laws are nonlinear, isotropic and homogeneous hyperelastic, normally used in mechanical analysis of elastomers, with the near compressibility assumption. It is applied the Flory decomposition, i.e., the multiplicative split of the deformation gradient into a volumetric and an isochoric part. A parallel processing strategy is used to increase the simulation speed and memory capacity, justifying the use of high order elements for solid analysis. Results confirm that the developed computer code is capable of predicting the static behavior of complex problems, such as Cook's membrane and partially loaded block. The shape functions generator code exhibits simplicity and, thus, it may be easily implemented in other finite elements. The increase in the order of approximation and the mesh refinement improve accuracy and, therefore, the proposed methodology together with parallel computing indicate a safe way for further developments in plasticity and damage mechanics for large strain and deformations.

Quasistatic inflation processes within rigid tubes

AbstractIn this paper the authors consider mechanical devices of rotational symmetry that can be seen as segments of an artificial worm or as a balloon for angioplasty. Continuing former work [7] the segment is now placed within a cylindrical or constricted rigid tube that will be touched or pressed during inflation of the segment. Both the segment's shape and the forces of contact are investigated. The main mathematical tool is the Principle of Minimal Potential Energy – handled as an optimal control problem with state constraint. The necessary optimality conditions are carefully analyzed and simulation results for characteristic examples are presented. The treatment of the problem is primarily mathematical but aiming at application.

Numerical simulation of dense particle-gas two-phase flow using the minimal potential energy principle

A simulation method of dense particle-gas two-phase flow has been developed. The binding force is introduced to present the impact of particle clustering and its expression is deduced according to the principle of minimal potential energy. The cluster collision, break-up and coalescence models are proposed based on the assumption that the particle cluster are treated as one discrete phase. These models are used to numerically study the two-phase flow field in a circulating fluidized bed (CFB). Detailed results of the cluster structure, cluster size, particle volume fraction, gas velocity, and particle velocity are obtained. The correlation between the simulation results and experimental data justifies that these models and algorithm are reasonable, and can be used to efficiently study the dense particle-gas two-phase flow.

Qualitative study of cavitated bifurcation for a class of incompressible generalized neo-Hookean spheres

The problem of spherical cavitated bifurcation was examined for a class of incompressible generalized neo-Hookean materials, in which the materials may be viewed as the homogeneous incompressible isotropic neo-Hookean material with radial perturbations. The condition of void nucleation for this problem was obtained. In contrast to the situation for a homogeneous isotropic neo-Hookean sphere, it is shown that not only there exists a secondary turning bifurcation point on the cavitated bifurcation solution which bifurcates locally to the left from trivial solution, and also the critical load is smaller than that for the material with no perturbations, as the parameters belong to some regions. It is proved that the cavitated bifurcation equation is equivalent to a class of normal forms with single-sided constraints near the critical point by using singularity theory. The stability of solutions and the actual stable equilibrium state were discussed respectively by using the minimal potential energy principle.

Study on cavitated bifurcation problems for spheres composed of hyper-elastic materials

In this paper, spherical cavitated bifurcation problems are examined for incompressible hyper-elastic materials and compressible hyper-elastic materials, respectively. For incompressible hyper-elastic materials, a cavitated bifurcation equation that describes cavity formation and growth for a solid sphere, composed of a class of transversely isotropic incompressible hyper-elastic materials, is obtained. Some qualitative properties of the solutions of the cavitated bifurcation equation are discussed in the different regions of the plane partitioned by material parameters indicating the degree of radial anisotropy in detail. It is shown that the cavitated bifurcation equation is equivalent, by use of singularity theory, to a class of normal forms with single-sided constraint conditions at the critical point. Stability and catastrophe of the solutions of the cavitated bifurcation equation are discussed by using the minimal potential-energy principle. For compressible hyper-elastic materials, a group of parameter-type solutions for the cavitated deformation for a solid sphere, composed of a class of isotropic compressible hyper-elastic materials, is obtained. Stability of the solutions is also discussed.

Variational Principles of Contact Elastostatics

In this paper, the variational principles of contact elastostatics, which were proposed and proved by Fichera (1964) and Duvaut & Lions (1972) are developed in an engineering fashion without use of functional analysis. The theory contains a number of new elements, but the elegant existence proofs of the French-Italian school are missing. A start is made by extending the principle of virtual work to normal and frictional contact in such a manner that it needs no longer be known beforehand whether—in the case of normal contact—actual contact is or is not established, or—in the case of frictional contact—slip does or does not occur. Then the principle of minimal potential energy is set up for a non-linear elastic body in contact with a rigid base. Uniqueness and minimality of the solution are proved under certain conditions, the Reissner principle is established, and the principle of minimal complementary energy is derived. Finally the principles are cast hi what is termed surface mechanical form, and two examples are given: the variational principle for normal half-space contact problems, and a new principle for time-dependent frictional half-space contact. Upon discretization, these principles provide a quadratic object function to be minimized under linear or quadratic inequality constraints. The positions of the contact area and of the regions of slip and adhesion appear as by-products of the calculation.