بهروز حسنی

The isogeometric method was introduced to bridge the gap between computer-aided design (CAD) and analysis. This method offers advantages such as precise geometric modeling, suitable refinement methods, easy access to higher-order functions, and higher computational accuracy. The aim of this research is to provide an efficient method for applying the distributed loads on curved surfaces in isogeometric analysis. One of the main challenges in this method is how to apply boundary conditions on complex geometries. In curved models, some control points may not lie on the geometry, leading to ambiguity in the distribution of loads on these points. This study uses NURBS functions, which are standard non-interpolatory functions in CAD systems, to approximate the solution space and describe the geometry. Additionally, to leverage the capabilities of CAD tools, the process of importing geometries created in Rhino into isogeometric analysis using Bézier extraction is explained. The results confirm the accuracy and efficiency of the proposed method.

Flexure joints are one of the most widely used and crucial elements in the design of precision mechanisms. Owing to their monolithic and elastic structure, these joints facilitate highly precise movements. In this study, we present a kinetoelastic model for designing various types of flexure joints with single and multiple degrees of freedom. To reduce computational costs, two beneficial approaches for defining the objective function and constraints are presented, based solely on the strain energy criterion and predetermined displacements. The resulting self-adjoint optimization problem exhibits computational efficiency and improved convergence. The topology optimization problem utilizes the Finite Element Method (FEM) and the Solid Isotropic Material with Penalization (SIMP) model, employing the Method of Moving Asymptotes (MMA) to solve and identify the optimal topology. A comprehensive mathematical framework, including the relevant two-dimensional (2D) boundary conditions and sensitivity analysis, is meticulously developed and extensively examined. For this purpose, MATLAB code is developed for designing 2D flexure joints with single and multiple degrees of freedom. Finally, the results obtained from the comparison of two optimization approaches presented in this study are discussed. In these joints, the stiffness ratio of the structure has increased significantly, up to 208 times, indicating the practicality and effectiveness of this method in the topology optimization of flexure joints.

In this paper, the isogeometric analysis of shell structures along with the optimal method for accurate calculation of nodal vectors is proposed. The Nurbs surface with maximum regularity is used for shell mid-surface description. According to the Reisner- Mindlin hypothesis, the director vectors at control points are needed for the interpolation of the rotations. The calculated nodal direct vectors must lead to exact interpolated director vectors on the shell surface. Hence, a method has been proposed in which the components of director vectors at control points are obtained by solving a system of equations on the whole patch. The system of equations is formed using known values of direction vectors at the Greville points. The accuracy of the proposed method has been investigated by using the results of the most common problem in shell analysis. Convergence behavior for displacement at the loading points has been studied in all solved problems for different order of NURBS and net of control points. The deformation results show better convergence behavior with increasing the regularity and order of NURBS. The knot averages are in a one-to-one correspondence with control points. Thus, the system of equations on these points leads to a unique solution for the nodal direction vectors, and the time to solve equations is significantly reduced.

Investigation of effects of the piezoelectric shear actuator on the static response of cross-ply laminated composite smart shells by using the isogeometric approach is the subject of this paper. In the analysis of laminated smart shells, the Mindlin-Reissner theory (first-order shear deformation theory) is used. The isogeometric approach has here been employed that utilizes the Non-Uniform Rational B-Splines (NURBS) of various orders to approximate the variables defining the geometry of smart shell as well as the unknown functions. In this research, the effect of different boundary conditions on structural transverse deformation by applying electric field has been studied. In the considered cases, smart shells possess two simply supported parallel edges while the other two edges are considered as a combination of free, clamped or simple supports. Also, study of the shear effects of the piezoelectric actuator on various factors, including the radius of curvature of the shell as well as the simultaneous mechanical and electrical loadings are amongst the objects of this article. To demonstrate the efficiency and accuracy of the isogeometric approach in the study of shear effects of the piezoelectric actuators, several numerical examples are presented and the obtained results indicate the desirability of the proposed approach.

In most of the structural optimization approaches analysis and sensitivities are carried out by using the conventional finite element method. Due to the variations of the problem geometry within the shape optimization iterations, updating the computational model by several remeshings is required that is quite time consuming and computationally costly. As a remedy for this problem, the NURBS-based isogeometric analysis method is here adopted that combines the Computer Aided Design (CAD) and finite element techniques. In this study, in the shape optimization of the structures the Method of Moving Asymptotes (MMA), which is a gradient-based method, is employed and to calculate the required sensitivities a fully analytical approach is presented. To demonstrate the performance of the suggested approach, various numerical examples are solved.

This paper presents isogeometric analysis of free form shells based on Kirchhoff-Love and Reissner-Mindlin theories. The isogeometric approach utilizes Non-Uniform Rational B-Splines (NURBS) for different order approximation of the variables defining the geometry as well as the unknown functions. The geometry is defined for both theories by the NURBS technique for surface generation. In the employed Reissner-Mindlin shell theory, by making use of the anchor point concept the normal vector is calculated accurately. The Kirchhoff-Love shell theory uses three displacements degrees of freedom per node, but the Reissner-Mindlin theory uses five degrees of freedom, three displacements and two rotations. Also, for Kirchhoff-Love shell theory C1 continuity of the NURBS basis functions is needed, while for the Reissner-Mindlin shell theory C0 continuity is sufficient. Several standard benchmark examples with available analytical solutions are presented to demonstrate the performance and accuracy of the approaches. Also, a new benchmark problem is designed to study the performance of the methods as well as the convergence behavior of the presented approach when applied to completely free form shells.

Isogeometric analysis is a new approach in computational mechanics where the geometry and computational modeling is carried out by using NURBS and B-spline functions. The main advantage of the isogeometric approach is in unifying the discretization and problem-solving processes that lead to saving of computational time and cost. In this research, the governing equations of buckling analysis of thin plates stiffened with stiffeners with various geometries are obtained by use of the variational accounting method and first-order shear deformation theory (FSDT). The geometry of stiffener and its position on arbitrarily plate are considered. The equation of buckling is derived by employing the total potential energy, and the obtained system of equations is solved by discretization with the isogeometric analysis method. One of the main advantages of this approach is that it does not need a fine mesh for unification of the connection between the plate and its stiffeners so that, it leads to more accurate answers in comparison with other numerical methods and commercial software with the same number of unknowns. Finally, In order to verification, a few examples are presented and the obtained results are compared with the available results of the analytical and numerical method.

Employing the Isogeometric Analysis method for solution of nonlinear compressible elastic materials, generally known as hyperelasticity, is the subject of this article. For this purpose, the matrix of coefficients is derived and by the linearization of governing equations the discretized equilibrium equations are obtained and a solution algorithm is presented. To study the performance and accuracy of the method in compressible hyperelastic problems, the obtained results are compared with those of finite elements. The presented approach, besides providing a good flexibility in geometrical modeling, results in a smaller system of equations and consequently reducing the computational cost. Furthermore, despite having large deformations, the need for remeshings is alleviated. Also, the effects of the number of load increments, as well as, the number of Gauss integration points on the convergence of the solution are studied.

This paper presents an improved approach for handling stress constraints in minimum weight topological design. The Finite Element Method (FEM) and the material model of Solid Isotropic Material with Penalization (SIMP) is used to formulate the topology optimization problem. To evaluate the stress values in elements, the von Mises stresses are calculated at the so called super-convergent Gauss quadrature points. To reduce the time and computational cost, a clustering approach is here adopted and the P-norm integrated stress constraints are used. Doing this, a large number of local constraints are replaced with a few global ones and consequently the stress constraint sensitivities are calculated by using the adjoint method. The employed formulation as well as a complete explanation of the sensitivity analysis is provided. Due to the complexity of the topology optimization problem in the presence of stress constraints, the Method of Moving Asymptotes (MMA) is here employed. To demonstrate the performance and capability of the procedure, a couple of plane stress elasticity problems are taken into consideration. The resulted layouts indicate the superiority of the approach in generating acceptable and practical topological designs.

This paper presents an isogeometric analysis approach for static and free vibration analysis of laminated composite plates covered with piezoelectric layers using the Reissner-Mindlin theory. Isogeometric analysis (IGA) aims at simplifying the Computer Aided Design (CAD) and Computer Aided Engineering (CAE) by using the functions describe the geometry (CAD) and the unknown fields (Analysis). The isogeometric approach has here been employed that utilizes the Non-Uniform Rational B-Splines (NURBS) of quadratic, cubic and quartic orders to approximate the variables defining geometry as well as the unknown functions. Using the Reissner-Mindlin first order shear deformation theory requires the C0-continuity of generalized displacements and the NURBS basis functions are well suited for this purpose. The electric potential is assumed to vary linearly through the thickness for each piezoelectric sublayer. To alleviate the shear locking problem, a stabilization technique is employed in the stiffness formulation. Since study of the performance and accuracy of IGA in solving laminated composite plates is one of the main objectives of this article. Several numerical examples are presented and compared with those available in the literature. The obtained results indicate desirable accuracy and efficiency of the proposed approach.

In this paper, the thermos-electro mechanical behavior of piezoelectric laminate shell has been studied by isogeometric analysis. Isogeometric analysis (IGA) is based on geometry generation technique, such as nurbs and splines. In Isogeometric analysis, same basis functions employed for geometry and approximation of the unknown field, unlike finite element method. In this paper, the analysis of composite shell structure is based on first-order shear deformation theory (Mindlin-Reissner), therefore each control point has five degrees of freedom, three displacement degrees of freedom and two rotations. For modeling of the electric field, we assume the variation of electric potential is linear through the thickness of piezo electric layers. The current work is validated though solving typical examples. For the Scordelis-Lo-Roof, maximum error is 0.066% that take place at the midpoint of free edge and for clamped shell maximum error is 0.039%. In other case studies, the goal is to achieve desired shape deformation by applying voltage. First by increasing the voltage on laminate shell under uniform load, the out of plane deformation has been eliminate. In continue, for control of thermal distortion, the symmetric and antisymmetric composite shell exposed to temperature gradient. By applying the voltage with same or opposite polarity, thermal twist or thermal bending has been compensated.

In this research, for the first time, the net of control points in the isogeometric analysis has been improved by employing an error estimator based on a stress recovery method. First, an error estimation algorithm based on stress recovery is used to obtain the energy norm for each element. Then, artificial rods are defined between control points and the estimated values of errors in the control points located at the vicinity of a typical point is assigned to each rod as a thermal gradient. Now, by analyzing this hypothetical truss problem under temperature changes a new arrangement of control points and consequently the knot vectors can be obtained. Repeating this process in isogeometric analysis will lead to a better distribution of errors in the domain of the problem and results in an optimal net of control points to calculate the integrals. To evaluate the efficiency of this method, the results of modeling and analysis of two elasticity problem is presented. The obtained results show that this innovative approach has a good performance and can be employed for reducing the analysis errors.

In this study, experimental study of profile geometry effect on Polycrystal Diamond Compact (PDC) drill bits performance and durability was conducted. In an extensive field study, three samples of bits was choosed among NIOC bits collection. PDC bit profile consists of apex, cone, nose, shoulder and gage, which all are effective on stability, penetration rate, aggressiveness and durability. Verification of the effect of PDC bit profile geometry needs to first determine the exact geometry. Complicated geometry of these PDC bits was obtained by 3D-scan and cloud of points. Then cutters arrangement of the profile was produced. In experimental study, field test of these bits was conducted in same condition (WOB, ROP, fluid velocity and drilling mud weight) in Ahwaz oil rig in Asmari formation. Drilling metrage and penetration rate was measured and the bits dull grading based on IADC standards was determined. Results of the bits test showed the effect of profile geometry on PDC bits performance and durability. optimization of profile geometry of PDC bits causes an increase in penetration rate, stability and durability.

This article is devoted to the derivation of formulation and isogeometric solution of nonlinear incompressible elastic problems, known as incompressible hyperelasticity. After problem definition, the governing equations are linearized for employing the Newton-Raphson iteration method. Then, the problem is discretized by using concepts of isogeometric analysis method and its solution algorithm is devised. To demonstrate the performance of the proposed approach, the obtained results are compared with finite elements. Due to large deformations in this kind of problems, the finite element method requires a relatively large number of elements, as well as the need for remeshings in some problems, that results in a large system of equations with a high computational cost. In the isogeometric analysis method, using B-Spline and NURBS (Non-Uniform Rational B-Spline) basis functions provides us with a good flexibility in modeling of geometry without any need for further remeshings. The examples studied in this article indicate that by using the isogeometric approach good quality results are obtained with a smaller system of equations and less computational cost. Also, influence of Gauss integration points for the incompressible materials are investigated.

A method for error estimation of isogeometric analysis of plane stress problems, based on stress recovery by using the super convergent properties of the Gauss points, was introduced. In this paper, a different approach for improvement of stresses based on the satisfaction of equilibrium equations by taking into consideration of two elasticity problems is followed and the effect of the number of the Gauss quadrature points is studied. In this approach, the equilibrium equations are satisfied for each patch of the isogeometric analysis model and it has been shown that the recovered stresses are more accurate than the previous method where the super-convergent properties were used. To demonstrate the performance and efficiency of the method a couple of elasticity problems are considered and the obtained results are compared with the previous method and exact solutions. The results indicate that the suggested method can be employed for error estimation and stress recovery in the isogeometrical analysis method.

This article is devoted to the derivation of formulation and isogeometric solution of nonlinear nearly incompressible elastic problems, known as nearly incompressible hyperelasticity. After problem definition, the governing equations are linearized for employing the Newton-Raphson iteration method. Then, the problem is discretized by using concepts of isogeometric analysis method and its solution algorithm is devised. To demonstrate the performance of the proposed approach, the obtained results are compared with finite elements. Due to large deformations in this kind of problems, the finite element method requires a relatively large number of elements, as well as the need for remeshings in some problems, that results in a large system of equations with a high computational cost. In the isogeometric analysis method, using B-Spline and NURBS (Non-Uniform Rational B-Spline) basis functions provides us with a good flexibility in modeling of geometry without any need for further remeshings. The examples studied in this article indicate that by using the isogeometric approach good quality results are obtained with a smaller system of equations and less computational cost. Also, influence of different volumetric functions for the nearly incompressible materials are investigated.

This research is devoted to the adaptive solution and control point net improvement of axisymmetric problems in isogeometric analysis using the error estimation based methods for stress recovery. For this purpose، after the calculation of the energy norm، the estimated value of error in the vicinity of each control point is assigned to the neighboring members of a hypothetical truss-like structure as an artificial thermal gradient. By analysis of this network of rods under the temperature variations a new arrangement of control points is obtained. Repeating this process of thermal isogeometric analysis will eventually lead to a better distribution of errors in the domain of the problem and results in an optimal net of control points for the calculation of the integrals. To demonstrate the performance and efficiency of the proposed method، two axisymmetric elasticity problems with available analytical solutions are considered. The obtained results indicate that this innovative approach is effective in reducing errors of axisymmetric problems and can be employed for improving the accuracy in the context of the isogeometric analysis method. Innovated method of this research focuses on adaptive analysis and Network improving of axisymmetric problems in isogeometric analysis using error estimation methods based on stress recovery. For this purpose after calculation the energy norm، estimated value of error in the vicinity of control points is assigned to each rod as the thermal gradient. Thus after analyzing the hypothetical rods network under the temperature changes a new arrangement of control points and knot vectors can be obtained. The use of multi-cycle of this process in isogeometric analysis will lead to a better distribution of errors in the domain and thus achieve optimal network to calculate the integrals. To measure the efficiency of this method and demonstrate the increased carefully in axisymmetric problems، which has the analytical solution، two elasticity problem is evaluated. The results show that innovative network improving method has good efficiency to reduce the error rate and can be used to increase the accuracy of isogeometric analysis results. Innovated method of this research focuses on adaptive analysis and Network improving of axisymmetric problems in isogeometric analysis using error estimation methods based on stress recovery. For this purpose after calculation the energy norm، estimated value of error in the vicinity of control points is assigned to each rod as the thermal gradient. Thus after analyzing the hypothetical rods network under the temperature changes a new arrangement of control points and knot vectors can be obtained. The use of multi-cycle of this process in isogeometric analysis will lead to a better distribution of errors in the domain and thus achieve optimal network to calculate the integrals. To measure the efficiency of this method and demonstrate the increased carefully in axisymmetric problems، which has the analytical solution، two elasticity problem is evaluated. The results show that innovative network improving method has good efficiency to reduce the error rate and can be used to increase the accuracy of isogeometric analysis results.

Study of the critical buckling load as well as post-buckling behavior of single-walled nanotubes (SWNT) under various thermal conditions is the subject of this article. For finding critical buckling loads the clamped-free and simply supported conditions are considered and for post-buckling analysis the boundary conditions are assumed to be clamped. A space-frame model is here employed for the zigzag and armchair nanotubes with different chiralities and aspect ratios. In this approach، the linkage between carbon atoms is modeled as three dimensional elastic beam. By establishing a linkage between structural mechanics and molecular mechanics، the sectional property parameters of these beam members are obtained. The obtained results indicate that، as it is expected، by increasing the aspect ratio of the nanotubes as well as chirality، the critical buckling load decreases. Also، it is noticed that the post-buckling behavior of both armchair and zigzag nanotubes are quite similar. In addition، the effect of temperature on the critical buckling load is investigated. Due to the influence of temperature over the linkage length and force field constants it is shown that when the temperature increases a decline in the critical buckling loads is observed.

Abstract Isogeomteric Analysis is a newly developed method with some features that can be considered as ‎a potential substitute to other numerical methods such as finite elements and meshless approaches. ‎The NURBS technique, that allows precise geometrical modeling, plays an important role in this ‎method. However, similar to other numerical methods, existence of errors in the approximation of ‎the unknown function is inevitable. This paper is devoted to finding points with higher accuracy in ‎stress recovery by the isogeometric analysis. It can be shown that these points are coincident with ‎the Gauss quadrature points. By making use of these superconvergent points together with the ‎NURBS technique and the least square method, a surface is constructed for each component of ‎the stress tensor that represents the improved stresses. For this purpose, three examples with ‎available analytical results has been solved. The comparison of the obtained improved stresses ‎with the exact solution is used for the sake of verification of the proposed method. It is concluded ‎that the superconvergent points location in the isogeometric analysis are the same as the minimum ‎required Gauss points for the integration of a square element.‎

A method for error estimation of isogeometric analysis of plane stress problems which is the based on stress recovery and using the super convergent properties of the Gauss points، has been already introduced. This paper is devoted to the development of the method and study of the effects of these supercovergent points on the solution improvement and error estimation of axisymmetric problems by the isogeometric analysis method. It is concluded that by using these optimal points for stress recovery and error estimation by isogeometric analysis a considerable improvement is attained.

Shape optimization of free form shell structures with different objective and constraint functions including the stress constraint is the subject of this article. To construct the geometry B-Splines are employed that allow generating smooth free form geometries with a small number of parameters which are considered as the design variables of the optimization problem. For analysis, the finite element method by using the Wilson’s quad shell element is employed. For shape optimization, in each step of the optimization process the mesh generation, finite element analysis, sensitivity analysis and geometry update steps are repeated until convergence. Maximization of the stiffness of structure with volume constraint and the minimization of the weight of structure with the von Misses stress constraint are the addressed problems of this article. In both kinds of problems, the applicates of the control points are considered as the design variables of the shape optimization problem and the sequential quadratic programming (SQP) is employed to solve the optimization problem. Since in this approach, the derivatives of the objective and constraint functions are needed, the sensitivity analysis is carried out in each step by the finite difference method. The quality and smoothness of the obtained results together with the convergence graphs of the presented examples are indicative of the usefulness and efficiency of the proposed approach for shape optimization of shell structures.

Study of the effect of confinement of concrete on the seismic performance and behavior of permanent shuttering concrete panel structures is the subject of this paper. For this purpose، a few building models with different heights، but similar planar layout of walls، with and without considering the effect of confinement، i. e. execution of boundary elements، are taken into consideration. For this study، the PERFORM 3D software is employed for the modeling of nonlinear behavior of these structures by the possibility of using a multi layer shell element with fiber sections. For finite element modeling of these sections two types of concrete fibers، confined and non-confined، are employed. After modeling and carrying out nonlinear analyses، performance of each of specimens at two different risk levels is determined. The obtained results indicate that although execution of the boundary elements in these structural systems does not considerably improve the seismic performance but the confinement is a major factor in improving some parameters such as ductility، the probable maximum strength and the loss of energy that have a positive influence on the seismic performance of the structure.

An isogeometrical approach, based on using the superconvergent property of the Gauss integration points, for error estimation and stress recovery of two-dimensional problems was introduced by Hassani et. al. In this paper, the method is further developed to deal with the isogeometrical analysis of three-dimensional problems. To investigate the performance of the approach in using the optimal stress points, two 3D examples with available analytical solutions are taken into consideration. The obtained results are indicative of the good performance of the method in improvement of stress and error estimation of 3D problems in the isogeometric analysis method.

The element-free Galerkin method which is enriched intrinsically is applied for fracture analysis of functionally graded materials under mode I steady-state and transient thermal loading. The stress intensity factors are evaluated by means of both equivalent domain integral and displacement correlation technique. Continuum functions and the micromechanical model are used to describe the distribution of material properties. For thermal shock analysis, the modal decomposition method which is a semi-discretization approach is implemented to obtain the transient temperature field. The accuracy of numerical results is verified using the available reference solutions. Also, few parametric analyses are performed to study the effect of material gradation on the stress intensity factors. The results imply that the magnitude of the stress intensity factor reaches to its peak at a short while after the thermal shock which indicates its significant role in the fracture failure.