Computational Mechanics

This study explores the hydrodynamic and aerodynamic performance of a submarine and an airfoil under various angles of attack (AoA) using advanced computational fluid dynamics (CFD) simulations. The incompressible Reynolds Averaged Navier-Stokes (RANS) equations were solved using ANSYS, leveraging its segregated flow solver and adjoint optimization capabilities to automate the creation and meshing of computational domains. By analyzing velocity and pressure distributions across coarse and fine mesh resolutions, the research highlights the superior accuracy of fine meshes in capturing complex flow phenomena, such as flow separation, wake behavior, and velocity gradients. Submarine simulations with control surfaces revealed distinct symmetries and nearly zero maneuvering coefficients for specific configurations, filling gaps in the existing literature on fully appended geometries. Optimization efforts led to an enhanced design with improved aerodynamic efficiency, achieving reduced drag and stabilized flow, as validated by consistent performance at AoAs of 0°, 20°, and 80°. This work demonstrates the importance of fine mesh resolution, automated workflows, and adjoint solvers in accelerating the iterative design process and optimizing marine and aerodynamic structures for real-world applications. These findings highlight the significant influence of high attack angles on the submarine's vertical plane flow. Such insights offer a mechanical foundation for analyzing nonlinear motion phenomena during submarine surfacing. .

Despite the growing acceptance of SOA, service-oriented computing remains a computing mechanism to speed-up the design of software applications by assembling ready-made services. We argue that it is difficult for business people to fully benefit of the SOA if it remains at the software level. The paper proposes a move towards a description of services in business terms, i.e. intentions and strategies to achieve them and to organize their publication, search and composition on the basis of these descriptions. In this way, it leverages on the SOA to an intentional level, the ISOA. We present ISM, the model to describe intentional services, and to populate the service registry. We highlight its intention driven perspective for service description, retrieval and composition. Thereafter, we propose a methodology to determine intentional services that meet business goals. Finally, we introduce agent architecture to support model driven execution of intentional services.

Modeling particle based heterogeneous materials using Statistical Volume Elements (SVE) for predicting its mechanical behavior can be tedious when the particles are densely packed or elongated. Positioning particles without creating overlaps and avoiding meshing problems are two obstacles frequently mentioned. To counter these obstacles, a new modeling methodology based on Multibody Dynamics (MBD) and on an erosion-based homogenization method is proposed. The CAD model of a SVE is first generated and particles causing meshing problems are excluded. Meshing and Finite Element Analysis (FEA) are automatically carried out and a subsequent erosion-based homogenization method is used to retrieve the macroscopic behavior of the SVE. To illustrate the potential of this new method, results obtained with a Random Sequential Adsorption algorithm on non-eroded SVEs are compared with results obtained from the same SVEs submitted to our erosion method. These results are then compared with results obtained using the new MBD based approach.

A multiscale simulation method is established to study the microstructural responses of near-surface grain boundary structures of copper subjected to ultrashort femtosecond laser pulse. By integrating a two-temperature model with molecular dynamics, the presented approach allows for incorporation of both laser processing parameters and microstructures, enabling systematic simulation studies on the process-properties link. Following a brief introduction of the simulation methodology, a detailed modeling study on the ultrashort laser-material interaction is presented. In particular, we highlight the effects of laser process parameters on the near-surface response and corresponding phase change, formation of voids and their growth, and mechanism of dislocation nucleating and propagating from grain boundary.

A multiscale space-time finite element method based on time-discontinuous Galerkin and enrichment approach is presented in this work with a focus on improving the computational efficiencies for high cycle fatigue simulations. While the robustness of the TDG-based space-time method has been extensively demonstrated, a critical barrier for the extensive application is the large computational cost due to the additional temporal dimension and enrichment that are introduced. The present implementation focuses on two aspects: firstly, a preconditioned iterative solver is developed along with techniques for optimizing the matrix storage and operations. Secondly, parallel algorithms based on multicore graphics processing unit are established to accelerate the progressive damage model implementation. It is shown that the computing time and memory from the accelerated space-time implementation scale with the number of degree of freedom N through ∼O(N 1.6 ) and ∼O(N ), respectively. Finally, we demonstrate the accelerated space-time FEM simulation through benchmark problems.

Generalized beam-column element on two parameter elastic foundation K. Morfidis, I.E. Avramidis a Dr civil engineer, lecturer, Dept. of Civil Engineering, Division of Structural Engineering, Aristotle University of Thessaloniki 540 06 Thessaloniki b Dr civil engineer, professor, Dept. of Civil Engineering, Division of Structural Engineering, Aristotle University of Thessaloniki, 540 06 Thessaloniki

The aim of this article is to study the accuracy of finite element simulations in predicting the tool force occurring during the single point incremental forming (SPIF) process. The forming of two cones in soft aluminum was studied with two finite element (FE) codes and several constitutive laws (an elastic-plastic law coupled with various hardening models). The parameters of these laws were identified using several combinations of a tensile test, shear tests, and an inverse modeling approach taking into account a test similar to the incremental forming process. Comparisons between measured and predicted force values are performed. This

Theoretical three-dimensional Gaussian heat distribution model of the complex heat flow and plasma properties of cutting plasma torches have been developed. For cutting metallic plates, plasma torches must produce a narrow supersonic plasma jet with enough energy and momentum densities to melt, vaporize, and remove the metal from the impingement region. Our model allows us to study the details of the heat distribution and to make predictions on pick temperature development on metal surface, heat transfer to the ...

Les joints de grains jouent un rôle primordial lors de la déformation élastique et élasto-plastique d'un polycristal. L'influence des joints est traditionnellement appréciée à différentes échelles : - à l'échelle microscopique, on considère les interactions entre les dislocations du réseau cristallin et les défauts propres constituant la microstructure des joints. Ce faisant on perd de vue les interactions à grande distance entre les grains, - à l'échelle macroscopique, on considère que l'influence des joints provient des effets des incompatibilités de déformation élastique et plastique entre les grains d'un agrégat polycristallin. Ce faisant, on perd de vue les phénomènes particuliers qui se produisent au niveau des joints du fait de leurs caractéristiques propres, en n'envisageant que des effets moyens de grains à grains. Les joints de grains sont à l'origine de la déformation hétérogène des grains. Cette hétérogénéité se manifeste par l'existen...

Metal Matrix Composites (MMCs) are widely used in several strategic industrial sectors, such as defense, aerospace, nuclear power plants, space exploration, being the main source of technological progress in the others, for example machining. In this communication, we use meshless method that is peridynamics for simulation of impact of a sample. Peridynamics is a non-local, meshless quite recently formulated method of stress analysis. Nonlocal methods were developed for crystal analysis [1], [2]. The nonlocal methods were generalized on the coupled problems in [3]. The peridynamics was formulated for the first time by Silling [4, 5].

Numerical viscosity has long been a problem in fluid animation. Existing methods suffer from intrinsic artificial dissipation and often apply complicated computational mechanisms to combat such effects. Consequently, dissipative behavior cannot be controlled or modeled explicitly in a manner independent of time step size, complicating the use of coarse previews and adaptive-time stepping methods. This paper proposes simple, unconditionally stable, fully Eulerian integration schemes with no numerical viscosity that are capable of maintaining the liveliness of fluid motion without recourse to corrective devices. Pressure and fluxes are solved efficiently and simultaneously in a time-reversible manner on simplicial grids, and the energy is preserved exactly over long time scales in the case of inviscid fluids. These integrators can be viewed as an extension of the classical energy-preserving Harlow-Welch / Crank-Nicolson scheme to simplicial grids.

Vibration analysis is an essential aspect of engineering design and diagnostics, critical for ensuring the safety, durability, and performance of mechanical and structural systems. This paper presents a comprehensive guide to the application of Finite Element Analysis (FEA) in vibration studies, covering three primary techniques: modal analysis, harmonic response analysis, and power spectral density (PSD) analysis. Each method is explored in depth, with practical examples demonstrating their roles in identifying resonance conditions, predicting structural responses under periodic and random excitations, and guiding design optimizations to mitigate vibrational risks. Case studies on pump assemblies, water gliders, and space structures (FPSS) showcase real-world applications, providing insight into how FEA enhances engineering reliability and operational efficiency. The study underscores the importance of simulation-based vibration analysis in modern engineering workflows and advocates for its integration into iterative design processes to preempt failures and extend service life across industries.

In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time evolution of several nonlinear optimality systems in many-query context, where a system must be analysed for various physical and geometrical features. Optimal control can be used in order to fill the gap between collected data and mathematical model and it is usually related to very time consuming activities: inverse problems, statistics, etc. Standard discretization techniques may lead to unbearable simulations for real applications. We aim at showing how reduced order modelling can solve this issue. We rely on a space-time POD-Galerkin reduction in order to solve the optimal control problem in a low dimensional reduced space in a fast way for several parametric instances. The proposed algorithm is validated with a numerical test based on environmental sciences: a reduced optimal control problem governed by viscous Shallow Waters Equations parametrized not only in the physics features, but also in the geometrical ones. We will show how the reduced model can be useful in order to recover desired velocity and height profiles more rapidly with respect to the standard simulation, not losing accuracy. Keywords. Reduced order modelling, optimal control problems, time dependent nonlinear partial differential equations, Lagrangian approach. This contribution is rooted in control systems and controllability theory for partial differential equation. A control problem is a system on which you can act through suitable external variables said controls . The controllability theory answers to the need of steering a system towards a desired configuration. Is it always possible? Under which conditions can I reach an exact prescribed profile for my system? The problem is quite fascinating and of utmost usefulness in many applications. Even if linear partial differential control systems have many complex aspects and features to be analyzed both theoretically and numerically , our main focus will concern nonlinearity in fluid dynamics. In this setting, the problem becomes more challenging and, besides the growing complexity, the need of a control tool increases. The case of nonlinear partial differential equations is much more complicated to handle. The control theory for fluid models, e.g. Navier-Stokes equations, prospered in the eighties thanks to the research of J. L. Lions. The main idea of his production relied on the role which nonlinearity plays as a control itself, giving the possibility or preventing the achievement of peculiar motion behaviours . This intuition paves the way to a wide range of literature which addresses the problem . However, in many applied contexts, it is clear that not all the systems are controllable and, furthermore, it is not possible to prove the existence of controls which give the exact desired solution profile one wants to reach. This is the reason why the controllabilty theory expands towards optimization and optimal control theory. Namely, the new objective is to find a way to reach the most similar configuration with respect to the desired one, satisfying the underling partial differential equation

In this work, stress analysis of a polymeric cylinder's cylindrical shell reinforced with carbon nanotubes (CNTs) is investigated. The cylinder is subjected to mechanical and thermal loadings. All the equivalent mechanical and thermal properties of nano-composite cylinder are obtained using Mori-Tanaka model. Based on equilibrium, the governing equation is derived. Using an exact solution, the stresses and radial displacement distributions in the structure are calculated. The effects of CNTs volume percent on the stresses and radial displacement for internal and external pressure cylinder are the main discussion of this study. Numerical results indicate that with increasing CNTs volume percent, the stresses decrease. However, this shows the important effect of nanotechnology in stress reduction of cylinder which may be useful in sensors and actuators.

Detection of biomarkers is exploited in lab-on-a-chip devices by means of Love type Surface Acoustic Waves (SAW). Finger type arrangement of electrodes, used for InterDigital-Transducers (IDT), perform well to create and detect SAW by using electro-mechanical coupling. Efficiency of such a transceiver depends on design parameters such as chosen material orientation, thickness, placement of electrodes. An optimized design reduces production costs, hence, we need a digital twin of the device with multiphysics simulations that compute deformation and electric field. In this study, we develop a framework with the open-source package called FEniCS for modal and transient analyses of IDTs by using the Finite Element Method (FEM). Specifically, we discuss all possible sensor design parameters and propose a computational design guideline that determines the "best" thickness parameter by maximizing mass sensitivity, thus, efficiency for a Love surface acoustic wave sensor. Lab-on-a-chip • Love-wave • Optimization • Mass-sensitivity • FEM • IDT B Bilen Emek Abali

Background The bone loss associated with revision surgery or pathology has been the impetus for developing modular revision total hip prostheses. Few studies have assessed these modular implants quantitatively from a mechanical standpoint. Methods Three-dimensional finite element (FE) models were developed to mimic a hip implant alone (Construct A) and a hip implant-femur configuration (Construct B). Bonded contact was assumed for all interfaces to simulate long-term bony ongrowth and stability. The hip implants modeled were a Modular stem having two interlocking parts (Zimmer Modular Revision Hip System, Zimmer, Warsaw, IN, USA) and a Monoblock stem made from a single piece of material (Stryker Restoration HA Hip System, Stryker, Mahwah, NJ, USA). Axial loads of 700 and 2000 N were applied to Construct A and 2000 N to Construct B models. Stiffness, strain, and stress were computed. Mechanical tests using axial loads were used for Construct A to validate the FE model. Strain gages w...

For the determination of effective elastic properties an energy averaging procedure has been used for particle reinforced composite materials. This procedure is based on ®nite element calculations of the deformation energy of a characteristic volume element. The proposed approach allows the determination of effective properties of particle reinforced composite with acceptable precision. The calculated effective properties of the composite are found in range between upper and lower Hashin-Shtrikman bounds. The averaging elastic properties of the composite depend on the properties of the particles, matrix volume fraction of the particles and some parameters taking into account the in¯uence of the interphase between matrix and particles. These dependencies can be presented by simple analytical functions approximatically. An identi®cation procedure basing on numerical experiments allows the estimation of the unknown approximation parameters. The obtained functions describe precisely the numerical data for any relationship between material constituents.

We use the algebraic orthogonality of rotation-free and divergence-free fields in the Fourier space to derive the solution of a class of linear homogenization problems as the solution of a large linear system. The effective constitutive tensor constitutes only a small part of the solution vector. Therefore, we propose to use a synchronous and local iterative method that is capable to efficiently compute only a single component of the solution vector. If the convergence of the iterative solver is ensured, i.e., the system matrix is positive definite and diagonally dominant, it outperforms standard direct and iterative solvers that compute the complete solution. It has been found that for larger phase contrasts in the homogenization problem, the convergence is lost, and one needs to resort to other linear system solvers. Therefore, we discuss the linear system's properties and the advantages as well as drawbacks of the presented homogenization approach.

This document summarizes research performed under the SNL LDRD entitled -Computational Mechanics for Geosystems Management to Support the Energy and Natural Resources Mission.‖ The main accomplishment was development of a foundational SNL capability for computational thermal, chemical, fluid, and solid mechanics analysis of geosystems. The code was developed within the SNL Sierra software system. This report summarizes the capabilities of the simulation code and the supporting research and development conducted under this LDRD.

We present a speculative but testable framework for addressing the P = NP problem using a novel computational paradigm called symbolic resonance collapse. By encoding NP-complete problems within a prime-based Hilbert space and evolving symbolic states through clause-consistent resonance operators, we define a deterministic symbolic transformer T res that achieves convergence without search. We formalize the symbolic entropy landscape, introduce clause-local resonance operators, and demonstrate convergence on small-scale instances. We provide explicit generalizations of our approach to multiple NP-complete problems including Subset Sum, Hamiltonian Path, and Vertex Cover, demonstrating the versatility of the symbolic resonance paradigm. Furthermore, we develop a universal symbolic transformer framework applicable to any problem in NP, unifying these results through a general formalism based on verifier projections. Through both problem-specific applications and our universal framework, we establish a coherent foundation for a constructive approach to addressing the P=NP question.

On the basis of intrinsic properties of the vector parameterization of rotational motions this work presents an explicit solution of the problem of decomposition of any finite rotation into a product of three successive finite rotations about prescribed axes.

Convolutional Neural Network (CNN) is one of the most important architectures in deep learning. The fundamental building block of a CNN is a trainable filter, represented as a discrete grid, used to perform convolution on discrete input data. In this work, we propose a continuous version of a trainable convolutional filter able to work also with unstructured data. This new framework allows exploring CNNs beyond discrete domains, enlarging the usage of this important learning technique for many more complex problems. Our experiments show that the continuous filter can achieve a level of accuracy comparable to the state-of-the-art discrete filter, and that it can be used in current deep learning architectures as a building block to solve problems with unstructured domains as well.

Convolutional Neural Network (CNN) is one of the most important architectures in deep learning. The fundamental building block of a CNN is a trainable filter, represented as a discrete grid, used to perform convolution on discrete input data. In this work, we propose a continuous version of a trainable convolutional filter able to work also with unstructured data. This new framework allows exploring CNNs beyond discrete domains, enlarging the usage of this important learning technique for many more complex problems. Our experiments show that the continuous filter can achieve a level of accuracy comparable to the state-of-the-art discrete filter, and that it can be used in current deep learning architectures as a building block to solve problems with unstructured domains as well.

We present a three-dimensional discrete-element approach for numerical investigation of wet granular media. This approach relies on basic laws of contact and Coulomb friction enriched by a capillary force law between particles. We show that the latter can be expressed as a simple explicit function of the gap and volume of the liquid bridge connecting a pair of spherical particles. The length scales involved in this expression are analyzed by comparing with direct integration of the Laplace-Young equation. We illustrate and validate this approach by application to direct shear and simple compression loadings. The shear and compression strengths obtained from simulations reproduce well the experimental measurements under similar material and boundary conditions. Our findings show clearly that the number density of liquid bonds in the bulk is a decisive parameter for the overall cohesion of wet granular materials. A homogeneous distribution of the liquid within the bridge debonding distance, even at low volume contents, leads to highest cohesion. The latter is independent of the liquid content as far as the liquid remains in the pendular state and the number density of liquid bonds remains constant.

We present a 3D discrete‐element approach for numerical investigation of wet granular media. This approach relies on the basic laws of contact and Coulomb friction enriched by a capillary force law between particles. We show that the latter can be expressed as a simple explicit function of the gap and volume of the liquid bridge connecting a pair of spherical particles. The length scales involved in this expression are analyzed by comparing with direct integration of the Laplace–Young equation. We illustrate and validate this approach by application to direct shear and simple compression loadings. The shear and compression strengths obtained from simulations reproduce well the experimental measurements under similar material and boundary conditions. Our findings clearly show that the number density of liquid bonds in the bulk is a decisive parameter for the overall cohesion of wet granular materials. A homogeneous distribution of the liquid within the bridge debonding distance, even...

We analyse the Coulomb cohesion of wet granular materials and its relationship with the distribution of capillary bonds between particles. We show that, within a harmonic representation of the bond and force states, the shear strength can be expressed as a state equation in terms of internal anisotropy parameters. This formulation involves a dependence of the shear strength on loading direction and leads to the fragile behaviour of granular materials. The contact dynamics simulations of a wet material, in which a capillary force law is prescribed, are in excellent agreement with the predictions of this model. We find that the fragile character decreases as the local adhesion is increased or the mean stress is decreased.

In the paper, the extended finite element method (XFEM) is combined with a recovery procedure in the analysis of the discontinuous Poisson problem. The model considers the weak as well as the strong discontinuity. Computationally efficient low-order finite elements provided good convergence are used. The combination of the XFEM with a recovery procedure allows for optimal convergence rates in the gradient i.e. as the same order as the primary solution. The discontinuity is modelled independently of the finite element mesh using a step-enrichment and level set approach. The results show improved gradient prediction locally for the interface element and globally for the entire domain.

This study investigated the various techniques available for rigid body system simulation, thus providing a thorough overview of the latest relevant literature. It became apparent that no engineering level accurate impulsive approaches for rigid body system simulation with concurrent contacts were in use or even existed up to now. A general formulation and solution technique for multiple concurrent contact problems were developed and tested on simple systems. Advantages of the formulation used are that the minimum of material properties, i.e. density, normal and tangential restitution coefficients and static and dynamic friction factors – all measurable, need to be specified and the results should be physically correct to a very high precision. Results obtained were encouraging and demonstrated that the original binary collision model available thus far could at least be extended to a heptenary simultaneous collision model.

The aim of the present study is to investigate the occurrence of transonic flow in several cascade geometries and blade sections that have been considered in the design of Wells turbine rotor blades. The calculations were performed using an implicit Euler solver for two-dimensional flow. The numerical method uses a multi-dimensional upwind matrix residual distribution scheme formulated on a new symmetrized form of the Euler equations, both in time and in space, that decouples the entropy and the enthalpy equations. Second-order accurate steady-state solutions where obtained using a compact three-point stencil. The results show that unwanted transonic flow may occur in the turbine rotor at relatively low mean-flow Mach numbers.

Compressed sensing is a signal compression technique with very remarkable properties. Among them, maybe the most salient one is its ability of overcoming the Shannon-Nyquist sampling theorem. In other words, it is able to reconstruct a signal at less than 2Q samplings per second, where Q stands for the highest frequency content of the signal. This property has, however, important applications in the field of computational mechanics, as we analyze in this paper. We consider a wide variety of applications, such as model order reduction, manifold learning, data-driven applications and nonlinear dimensionality reduction. Examples are provided for all of them that show the potentialities of compressed sensing in terms of CPU savings in the field of computational mechanics. Compressed sensing • Model order reduction • Manifold learning • Nonlinear dimensionality reduction 1 Introduction Model Order Reduction (MOR) is acquiring an utmost importance for simulation-based engineering. These techniques allow solving efficiently complex mathematical models, thanks to the use of adapted approximation bases to describe their solutions. Among the numerous existing B E. Cueto

The aim of this contribution is a comparison of different mapping techniques usually applied in the field of hierarchical adaptive FE-codes. The calculation of mechanical field variables for the modified mesh is an important but sensitive aspect of adaptation approaches of the spatial discretization. Regarding non-linear boundary value problems procedures of mesh refinement and coarsening imply the determination of strains, stresses and internal variables at the nodes and the Gauss points of new elements based on the transfer of the required data from the former mesh. The kind of mapping of the field variables affects the convergence behaviour as well as the costs of an adaptive FEM-calculation in a non-negligible manner. In order to improve the stability as well as the efficiency of the adaptive process a comparison of different mapping algorithms is presented and evaluated. Within this context, the mapping methods taken into account are -an element-oriented extrapolation procedure using special shape functions, -a patch-oriented transfer approach and, -the allocation of nodal history-dependent state (field) variable data using a supplementary integration of the material law at the nodes of the elements.

The aim of this contribution is a comparison of different mapping techniques usually applied in the field of hierarchical adaptive FE-codes. The calculation of mechanical field variables for the modified mesh is an important but sensitive aspect of adaptation approaches of the spatial discretization. Regarding non-linear boundary value problems procedures of mesh refinement and coarsening imply the determination of strains, stresses and internal variables at the nodes and the Gauss points of new elements based on the transfer of the required data from the former mesh. The kind of mapping of the field variables affects the convergence behaviour as well as the costs of an adaptive FEM-calculation in a non-negligible manner. In order to improve the stability as well as the efficiency of the adaptive process a comparison of different mapping algorithms is presented and evaluated. Within this context, the mapping methods taken into account are -an element-oriented extrapolation procedure using special shape functions, -a patch-oriented transfer approach and, -the allocation of nodal history-dependent state (field) variable data using a supplementary integration of the material law at the nodes of the elements.

The aim of this contribution is the presentation of an adaptive finite element procedure for the solution of geometrically and physically non-linear problems in structural mechanics. Within this context, the attention is mainly directed on the error estimation and hierarchical strategies for mesh refinement and coarsening in the case of finite elasto-plastic deformations. An important but sensitive aspect of adaptation approaches of the space discretization is the calculation of mechanical field variables for the modified mesh. Procedures of mesh refinement and coarsening imply the determination of strains, stresses and internal variables at the nodes and the Gauss points of new elements based on the transfer of the required data from the former mesh. In order to improve the efficiency as well as the convergence behaviour of the adaptive FE process an approach of data transfer primarily related to nodal values is presented. It is characterized by solving the initial value problem not only at the Gauss points but additionally at the nodes of the elements.

We show that in the variational multiscale framework, the weak enforcement of essential boundary conditions via Nitsche's method corresponds directly to a particular choice of projection operator. The consistency, symmetry and penalty terms of Nitsche's method all originate from the fine-scale closure dictated by the corresponding scale decomposition. As a result of this formalism, we are able to determine the exact fine-scale contributions in Nitsche-type formulations. In the context of the advection-diffusion equation, we develop a residual-based model that incorporates the non-vanishing fine scales at the Dirichlet boundaries. This results in an additional boundary term with a new model parameter. We then propose a parameter estimation strategy for all parameters involved that is also consistent for higher-order basis functions. We illustrate with numerical experiments that our new augmented model mitigates the overly diffusive behavior that the classical residual-based fine-scale model exhibits in boundary layers at boundaries with weakly enforced essential conditions.

The acceleration analysis of the slider crank mechanism using a new mathematical formulation is presented in this work. In this study, new kinematic response models of the slider crank mechanism were created. For the kinematic study of intricate mechanisms like the four-bar mechanism (slider crank), the new mathematical technique known as the Akozietic mathematical method, which uses trigonometric and inverse trigonometric functions, is appropriate. Using the equilibrium conditions of the forces in the mechanism, the Akozietic mathematical technique for a four-bar mechanism creates simple mathematical models that may be used to create user-written computer programs in Matlab and other programming languages. When the spreadsheet and this novel mathematical approach for mechanism analysis (Akozietic) were compared to standard numerical solutions in Mathematica, it was found that the new mathematical procedure created in this study outperformed the other two kinematic analysis approaches now in use. With the lowest link lengths, the spreadsheet approach stays relatively flat, suggesting less acceleration fluctuation. Greater forces will be applied to the slider in bigger configurations since the maximum acceleration of the slider is increased by increasing the lengths of the crank and connecting rod. The Akozietic method yields the highest numbers because of the lengthy crank and rod lengths, and the peak angular acceleration happens at 90°. The spreadsheet approach displays reduced numbers, emphasizing that shorter crank and rod lengths produce less angle.

The aim of this paper is to extend the applicability of an algorithm for solving inconsistent linear systems to the rank-deficient case, by employing incomplete projections onto the set of solutions of the augmented system Axr = b. The extended algorithm converges to the unique minimal norm solution of the least squares solutions. For that purpose, incomplete oblique projections are used, defined by means of matrices that penalize the norm of the residuals. The theoretical properties of the new algorithm are analyzed, and numerical experiences are presented comparing its performance with some well-known projection methods.

Global SLS-resolution is a well-known procedural semantics for top-down computation of queries under the well-founded model. It inherits from SLDNF-resolution the linearity property of derivations, which makes it easy and efficient to implement using a simple stack-based memory structure. However, like SLDNF-resolution it suffers from the problem of infinite loops and redundant computations. To resolve this problem, in this paper we develop a new procedural semantics, called SLTNF-resolution, by enhancing Global SLS-resolution with loop cutting and tabling mechanisms. SLTNFresolution is sound and complete w.r.t. the well-founded semantics for logic programs with the bounded-term-size property, and is superior to existing linear tabling procedural semantics such as SLT-resolution.

The extended finite element method combines the flexibility of mesh-independent discontinuities and the accuracy of singular enrichment functions. This paper introduces the method in the context of linear elasticity and gives an overview of its current state of research.