Izzet Ufuk Cagdas | Akdeniz University (original) (raw)

Papers by Izzet Ufuk Cagdas

Purpose-The purpose of this paper is to present the optimal design of a simply supported variable... more Purpose-The purpose of this paper is to present the optimal design of a simply supported variable curvature laminated angle-ply composite panel under uniaxial compression. The objective is to maximize the failure load which is defined as the minimum of the buckling load and the first-ply failure load. Design/methodology/approach-The numerical results presented are obtained using a shear deformable degenerated shell finite element, a brief formulation of which is given. Some verification problems are solved and a convergence study is conducted in order to assess the accuracy of the element. The design procedure is presented and optimization results are given for a simply supported symmetric eight layer angle-ply panel composed of a flat and two cylindrical sections. Findings-The influences of the stacking sequence and panel thickness on optimization are investigated and the effects of various problem parameters on the optimization procedure are discussed. Originality/value-The paper shows that the load carrying capacity of thicker panels is considerably reduced when the first-ply failure constraint is taken into account.

In this study, the influence of straight edge tangential restraints on the nonlinear response of ... more In this study, the influence of straight edge tangential restraints on the nonlinear response of symmetrically laminated and balanced composite cylindrical panels subject to a pinching force is investigated. An 8-node degenerated nonlinear shell element, formulation of which is based on the Total Lagrangian Formulation, is employed for geometrically nonlinear analysis and the Arc-Length Method is used to trace the nonlinear path. First, the element is validated for geometrically non-linear analysis by solving two verification problems. Then, numerical results for different rotational boundary conditions are presented for two different stacking sequences, and thickness values. The numerical results presented show that there is no significant difference between the tangentially unrestrained and restrained clamped panels when only one edge is tangentially unrestrained. However, it is observed that the simply supported panels demonstrate a much less stiff behavior when one of the straight edges is tangentially unrestrained.

Gazi Üniversitesi Fen Bilimleri dergisi, Jun 28, 2020

Politeknik dergisi, Mar 1, 2020

Bu çalışmada, eksenel basınç altındaki dik-katmanlı kompozit silindirlerin serbest titreşim davra... more Bu çalışmada, eksenel basınç altındaki dik-katmanlı kompozit silindirlerin serbest titreşim davranışları dönel atalet ve kalınlık/yarıçap oranını içeren birinci mertebeden uygun bir kayma deformasyonlu kabuk teorisine dayanan yarı-analitik bir sonlu eleman kullanılarak araştırılmıştır. Öncelikle, eksenel simetrik kabuk sonlu elemanının doğrulanması için bir çalışma yapılmış ve basıncın bulunmadığı haller için geliştirilmiş sonlu eleman ile elde edilmiş titreşim frekanslarının literatürde bulunan neti celer ile çok iyi uyum içinde olduğu görülmüştür. Aynı eleman ilk katman göçme analizi için de doğrulanmış ve kayma deformasyonlu bir eğri kabuk elemanı ile ile elde edilen ilk katman göçme yükleri ile iyi uyum gözlenmiştir. Daha sonra, çeşitli sınır şartları na sahip ve burkulma ve ilk katman göçme yüklerinden düşük olacak şekilde farklı düzeylerde eksenel basınca maruz kompozit silindirler için serbest titreşim analizleri yapılmıştır. Göz önünde bulundurulan silindirik yapıların temel titreşim frekanslarında karşı gelen burkulma yüklerinin % 60 ila 80 nispetinde eksenel yük değerleri için hızla azaldığı gözlemlenmiştir. Ayrıca, bazı nispeten kalın silindirlerde ilk-katman göçme yükünün burkulma yükünden az olduğu da belirlenmiştir.

International journal of computational and experimental science and engineering, Jul 31, 2019

In this study, the unimodal optimality conditions for axially compressed shear deformable columns... more In this study, the unimodal optimality conditions for axially compressed shear deformable columns are formulated and the optimal design problems defined are numerically solved using an iterative procedure based on the finite element method. The results presented show that the optimization results are more reliable than the ones obtained using classical beam theory as cross-sectional area does not vanish at points where the bending moment is equal to zero.

Gazi Journal of Engineering Sciences, 2019

Bu çalışmada cam elyaf takviyeli poliüretan dış yüzlü ve rijit köpük çekirdekli sandviç kiriş eği... more Bu çalışmada cam elyaf takviyeli poliüretan dış yüzlü ve rijit köpük çekirdekli sandviç kiriş eğilme rijitliğinin konsol kiriş titreşim testi ile belirlenmesi konusu üzerinde durulmuştur. İmal edilen sandviç kiriş numuneleri üzerinde yapılan konsol kiriş titreşim deneylerinden elde edilmiş eğilme rijitliği değerleri bir sonlu elemanlar modeli ile ve 3 nokta eğilme deneyi ile elde edilmiş olan değerler ile mukayeseli olarak sunulmuştur. Elde edilen neticeler kompozit sandviç kiriş eğilme rijitliğinin konsol kiriş titreşim deneyi ile 3 nokta yükleme deneyinden daha yüksek hassasiyetle belirlenebildiğini göstermektedir.

Journal of Cellular Plastics, 2022

In this study, a modified three rail shear test (or double shear test) procedure is described for... more In this study, a modified three rail shear test (or double shear test) procedure is described for the determination of the shear moduli and the shear strength values of rigid foamed materials and test results are presented for light extruded polystyrene, which is a typical core material used in sandwich construction. The main idea is to obtain a nearly uniform shear stress distribution in the shear test specimens by strengthening them against bending. First, using a finite element model, it is numerically shown that a nearly pure shear stress state may be obtained in the strengthened three rail shear test specimens. Then, it is shown that the finite element numerical results obtained for the strengthened specimens are in excellent agreement with the analytical results. Next, three rail shear tests are performed on bare and strengthened specimens and the experimental results obtained are presented in comparison with the analytical results. Also, clamped beam vibration and three-point...

Journal of Sandwich Structures & Materials, 2018

In this study, indentation of metal-faced and foam-cored sandwich beams under the action of quasi... more In this study, indentation of metal-faced and foam-cored sandwich beams under the action of quasi-static concentrated loads applied by using a flat punch is studied. First, a modified analytical expression yielding the pre-indentation load, which is based on plastic limit analysis, is developed. Then, indentation tests are conducted on specimens having extruded polystyrene core, and thin and laminated galvanized steel faces are developed to check the validity of the analytical expression. For the cases considered, the experimental results show that the analytical expression developed constitutes a lower bound to the true pre-indentation load. A parametric study is also conducted and the influences of the face sheet lamination parameters on the pre-indentation load are determined.

Composite Structures, 2017

In this study, filament wound truncated cones under axial compression are optimized with the obje... more In this study, filament wound truncated cones under axial compression are optimized with the objectives of minimizing the total weight and maximizing the failure load, which is defined as the minimum of the buckling and the first-ply failure (FPF) loads. The numerical results are obtained using an axisymmetric degenerated shell element based on a refined first-order shear deformable shell theory and a 2D degenerated shell element is used for verification purposes. It is shown that, FPF is more critical than buckling for thicker cones with lower cone angles. Optimal designs, where FPF and buckling are imposed as design constraints, are presented for filament wound cones using Micro-Genetic Algorithms. The results show that, using more layers having different winding angles has negligible influence on the failure load and the optimal design is not FPF critical for moderate levels of axial compression. The influence of the rotational boundary conditions on the optimal failure load is also demonstrated.

Ocean Engineering, 2017

The purpose of this paper is to present optimal designs for variable stiffness laminated composit... more The purpose of this paper is to present optimal designs for variable stiffness laminated composite truncated cones under lateral external pressure. The objective is to maximize the failure load which is defined as the minimum of the buckling load and the first-ply failure (FPF) load. The numerical results are obtained using a semi-analytical degenerated shell element based on a refined first-order shear deformable shell theory and the influences of the pressure stiffness (PS) and the thickness/radius ratio are taken into account. A 2D degenerated shell element is also used for verification purposes. Results are presented for the related verification problems solved and the semi-analytical shell element is validated. Optimal designs, where FPF and buckling are imposed as design constraints, are presented for laminated composite thin and relatively thick cones having variable thickness and ply-angle. A simple graphical optimization technique and a modified Micro-Genetic Algorithm are employed. It is shown that, FPF constraint may be active for thicker cones having lower cone angles, PS slightly decreases the buckling pressures, and the stacking sequence has considerable influence on the failure load. The numerical results presented show that restraining the large end against rotation significantly increases the failure load.

Journal of the Franklin Institute, 2007

Optimal piezo-actuator sizes and locations for a frame structure under bending load uncertainty a... more Optimal piezo-actuator sizes and locations for a frame structure under bending load uncertainty are determined with the objective of minimizing the deflection under worst case of loading. The bending moments generated by the piezo-actuators are used for deflection control, i.e., to minimize the maximum deflection. The frame is subjected to a tip load which lies in an uncertainty domain with regard to its magnitude and direction. The specific uncertain loading studied in the present paper involves a load of given magnitude but of unknown direction, which should be determined to produce the highest deflection. The worst case of loading depends on the size and location of the actuators leading to a nested problem of optimization (design) and anti-optimization (uncertainty problem). Results are given for deterministic and uncertain loading conditions.

The optimum designs are given for columns which are elastically clamped at both ends and under co... more The optimum designs are given for columns which are elastically clamped at both ends and under concentrated and distributed axial loads. The objective is to maximize the buckling load subject to volume and maximum stress constraints. The results for a minimum area constraint are also obtained for comparison. Under a distributed axial load, the stress constraint leads to different minimum

Procedia Engineering, 2011

ABSTRACT Curved panels are used extensively in several branches of engineering and in particular ... more ABSTRACT Curved panels are used extensively in several branches of engineering and in particular in marine and aerospace engineering working mostly under compressive loads. Failure of these components by buckling or excessive stress is an important design consideration. In the present study the effect of fiber orientation is studied on the failure load of a laminated curved panel subject to uniaxial compression. The failure modes are specified as first-ply failure and buckling with the failure load defined as the minimum of these two loads. The panel is taken as a symmetrically laminated angle-ply plate and the failure load is determined for different aspect ratios, panel thicknesses and boundary conditions (simply supported and clamped panels). The failure load is maximized for a set of selected stacking sequences by determining the best ply angle for each stacking sequence giving the highest failure load.

Thin-Walled Structures, 2011

A curved axisymmetric shell finite element based on a consistent first-order shear deformable she... more A curved axisymmetric shell finite element based on a consistent first-order shear deformable shell theory is developed for the linear stability analysis of cross-ply laminated shells of revolution under compressive loads. Finite element analysis results are presented for isotropic, orthotropic and cross-ply laminated shells of revolution in comparison with the analytical and numerical results found in the literature. These comparisons

Optimal Control Applications and Methods, 2009

ABSTRACT The optimum designs are given for columns, which are simply supported and under distribu... more ABSTRACT The optimum designs are given for columns, which are simply supported and under distributed and concentrated axial loads. The objective is to maximize the buckling load subject to volume and maximum stress constraints. The area of the minimum cross-section under a stress constraint is not known a priori as it depends on the maximum buckling load which in turn depends on the optimum shape. This minimum cross-sectional area is computed as part of an iterative procedure. An iterative solution method is developed based on finite elements and the results are obtained for n=1, 2, 3, defined as I =αnAn with I being the moment of inertia, and A the cross-sectional area. Numerical results show that the optimal areas become larger in the direction of the distributed load. Results are given for uniformly and triangular distributed loads, which are shown to have distinct effects on the optimal column shape. Copyright © 2009 John Wiley & Sons, Ltd.

Journal of Thermoplastic Composite Materials, 2013

In-plane prebuckling stresses arise under axial edge loading as a result of a plate boundary bein... more In-plane prebuckling stresses arise under axial edge loading as a result of a plate boundary being restrained from deformation in the plane of the plate. These stresses exhibit a uniform distribution only under a special set of boundary conditions and in general such uniform in-plane stress distributions do not exist under most boundary conditions encountered in practice. In the present study, in-plane prebuckling stresses are investigated for various in-plane boundary constraints and the stress contour lines are given for rectangular cross-ply laminated plates under linearly varying edge loads. The second part of the article involves the computation of the optimal layer thickness to maximize the buckling load under various combinations of in-plane boundary restraints. The numerical solutions are obtained by finite elements based on first-order shear deformable plate theory which include the in-plane deformations as nodal degrees of freedom. Numerical results show that the exclusion...

Journal of the Franklin Institute, 2007

Two algorithms based on an integral equation formulation of the buckling optimization problem are... more Two algorithms based on an integral equation formulation of the buckling optimization problem are formulated and implemented. The objective of the optimization is to maximize the buckling load of an elastically restrained column by optimally designing the cross-sectional area subject to a minimum cross-section or maximum stress constraint. The first approach involves solving the resulting integral equations iteratively taking into

Journal of Engineering Mechanics, 2013

Purpose-The purpose of this paper is to present the optimal design of a simply supported variable... more Purpose-The purpose of this paper is to present the optimal design of a simply supported variable curvature laminated angle-ply composite panel under uniaxial compression. The objective is to maximize the failure load which is defined as the minimum of the buckling load and the first-ply failure load. Design/methodology/approach-The numerical results presented are obtained using a shear deformable degenerated shell finite element, a brief formulation of which is given. Some verification problems are solved and a convergence study is conducted in order to assess the accuracy of the element. The design procedure is presented and optimization results are given for a simply supported symmetric eight layer angle-ply panel composed of a flat and two cylindrical sections. Findings-The influences of the stacking sequence and panel thickness on optimization are investigated and the effects of various problem parameters on the optimization procedure are discussed. Originality/value-The paper shows that the load carrying capacity of thicker panels is considerably reduced when the first-ply failure constraint is taken into account.

In this study, the influence of straight edge tangential restraints on the nonlinear response of ... more In this study, the influence of straight edge tangential restraints on the nonlinear response of symmetrically laminated and balanced composite cylindrical panels subject to a pinching force is investigated. An 8-node degenerated nonlinear shell element, formulation of which is based on the Total Lagrangian Formulation, is employed for geometrically nonlinear analysis and the Arc-Length Method is used to trace the nonlinear path. First, the element is validated for geometrically non-linear analysis by solving two verification problems. Then, numerical results for different rotational boundary conditions are presented for two different stacking sequences, and thickness values. The numerical results presented show that there is no significant difference between the tangentially unrestrained and restrained clamped panels when only one edge is tangentially unrestrained. However, it is observed that the simply supported panels demonstrate a much less stiff behavior when one of the straight edges is tangentially unrestrained.

Gazi Üniversitesi Fen Bilimleri dergisi, Jun 28, 2020

Politeknik dergisi, Mar 1, 2020

Bu çalışmada, eksenel basınç altındaki dik-katmanlı kompozit silindirlerin serbest titreşim davra... more Bu çalışmada, eksenel basınç altındaki dik-katmanlı kompozit silindirlerin serbest titreşim davranışları dönel atalet ve kalınlık/yarıçap oranını içeren birinci mertebeden uygun bir kayma deformasyonlu kabuk teorisine dayanan yarı-analitik bir sonlu eleman kullanılarak araştırılmıştır. Öncelikle, eksenel simetrik kabuk sonlu elemanının doğrulanması için bir çalışma yapılmış ve basıncın bulunmadığı haller için geliştirilmiş sonlu eleman ile elde edilmiş titreşim frekanslarının literatürde bulunan neti celer ile çok iyi uyum içinde olduğu görülmüştür. Aynı eleman ilk katman göçme analizi için de doğrulanmış ve kayma deformasyonlu bir eğri kabuk elemanı ile ile elde edilen ilk katman göçme yükleri ile iyi uyum gözlenmiştir. Daha sonra, çeşitli sınır şartları na sahip ve burkulma ve ilk katman göçme yüklerinden düşük olacak şekilde farklı düzeylerde eksenel basınca maruz kompozit silindirler için serbest titreşim analizleri yapılmıştır. Göz önünde bulundurulan silindirik yapıların temel titreşim frekanslarında karşı gelen burkulma yüklerinin % 60 ila 80 nispetinde eksenel yük değerleri için hızla azaldığı gözlemlenmiştir. Ayrıca, bazı nispeten kalın silindirlerde ilk-katman göçme yükünün burkulma yükünden az olduğu da belirlenmiştir.

International journal of computational and experimental science and engineering, Jul 31, 2019

In this study, the unimodal optimality conditions for axially compressed shear deformable columns... more In this study, the unimodal optimality conditions for axially compressed shear deformable columns are formulated and the optimal design problems defined are numerically solved using an iterative procedure based on the finite element method. The results presented show that the optimization results are more reliable than the ones obtained using classical beam theory as cross-sectional area does not vanish at points where the bending moment is equal to zero.

Gazi Journal of Engineering Sciences, 2019

Bu çalışmada cam elyaf takviyeli poliüretan dış yüzlü ve rijit köpük çekirdekli sandviç kiriş eği... more Bu çalışmada cam elyaf takviyeli poliüretan dış yüzlü ve rijit köpük çekirdekli sandviç kiriş eğilme rijitliğinin konsol kiriş titreşim testi ile belirlenmesi konusu üzerinde durulmuştur. İmal edilen sandviç kiriş numuneleri üzerinde yapılan konsol kiriş titreşim deneylerinden elde edilmiş eğilme rijitliği değerleri bir sonlu elemanlar modeli ile ve 3 nokta eğilme deneyi ile elde edilmiş olan değerler ile mukayeseli olarak sunulmuştur. Elde edilen neticeler kompozit sandviç kiriş eğilme rijitliğinin konsol kiriş titreşim deneyi ile 3 nokta yükleme deneyinden daha yüksek hassasiyetle belirlenebildiğini göstermektedir.

Journal of Cellular Plastics, 2022

In this study, a modified three rail shear test (or double shear test) procedure is described for... more In this study, a modified three rail shear test (or double shear test) procedure is described for the determination of the shear moduli and the shear strength values of rigid foamed materials and test results are presented for light extruded polystyrene, which is a typical core material used in sandwich construction. The main idea is to obtain a nearly uniform shear stress distribution in the shear test specimens by strengthening them against bending. First, using a finite element model, it is numerically shown that a nearly pure shear stress state may be obtained in the strengthened three rail shear test specimens. Then, it is shown that the finite element numerical results obtained for the strengthened specimens are in excellent agreement with the analytical results. Next, three rail shear tests are performed on bare and strengthened specimens and the experimental results obtained are presented in comparison with the analytical results. Also, clamped beam vibration and three-point...

Journal of Sandwich Structures & Materials, 2018

In this study, indentation of metal-faced and foam-cored sandwich beams under the action of quasi... more In this study, indentation of metal-faced and foam-cored sandwich beams under the action of quasi-static concentrated loads applied by using a flat punch is studied. First, a modified analytical expression yielding the pre-indentation load, which is based on plastic limit analysis, is developed. Then, indentation tests are conducted on specimens having extruded polystyrene core, and thin and laminated galvanized steel faces are developed to check the validity of the analytical expression. For the cases considered, the experimental results show that the analytical expression developed constitutes a lower bound to the true pre-indentation load. A parametric study is also conducted and the influences of the face sheet lamination parameters on the pre-indentation load are determined.

Composite Structures, 2017

In this study, filament wound truncated cones under axial compression are optimized with the obje... more In this study, filament wound truncated cones under axial compression are optimized with the objectives of minimizing the total weight and maximizing the failure load, which is defined as the minimum of the buckling and the first-ply failure (FPF) loads. The numerical results are obtained using an axisymmetric degenerated shell element based on a refined first-order shear deformable shell theory and a 2D degenerated shell element is used for verification purposes. It is shown that, FPF is more critical than buckling for thicker cones with lower cone angles. Optimal designs, where FPF and buckling are imposed as design constraints, are presented for filament wound cones using Micro-Genetic Algorithms. The results show that, using more layers having different winding angles has negligible influence on the failure load and the optimal design is not FPF critical for moderate levels of axial compression. The influence of the rotational boundary conditions on the optimal failure load is also demonstrated.

Ocean Engineering, 2017

The purpose of this paper is to present optimal designs for variable stiffness laminated composit... more The purpose of this paper is to present optimal designs for variable stiffness laminated composite truncated cones under lateral external pressure. The objective is to maximize the failure load which is defined as the minimum of the buckling load and the first-ply failure (FPF) load. The numerical results are obtained using a semi-analytical degenerated shell element based on a refined first-order shear deformable shell theory and the influences of the pressure stiffness (PS) and the thickness/radius ratio are taken into account. A 2D degenerated shell element is also used for verification purposes. Results are presented for the related verification problems solved and the semi-analytical shell element is validated. Optimal designs, where FPF and buckling are imposed as design constraints, are presented for laminated composite thin and relatively thick cones having variable thickness and ply-angle. A simple graphical optimization technique and a modified Micro-Genetic Algorithm are employed. It is shown that, FPF constraint may be active for thicker cones having lower cone angles, PS slightly decreases the buckling pressures, and the stacking sequence has considerable influence on the failure load. The numerical results presented show that restraining the large end against rotation significantly increases the failure load.

Journal of the Franklin Institute, 2007

Optimal piezo-actuator sizes and locations for a frame structure under bending load uncertainty a... more Optimal piezo-actuator sizes and locations for a frame structure under bending load uncertainty are determined with the objective of minimizing the deflection under worst case of loading. The bending moments generated by the piezo-actuators are used for deflection control, i.e., to minimize the maximum deflection. The frame is subjected to a tip load which lies in an uncertainty domain with regard to its magnitude and direction. The specific uncertain loading studied in the present paper involves a load of given magnitude but of unknown direction, which should be determined to produce the highest deflection. The worst case of loading depends on the size and location of the actuators leading to a nested problem of optimization (design) and anti-optimization (uncertainty problem). Results are given for deterministic and uncertain loading conditions.

The optimum designs are given for columns which are elastically clamped at both ends and under co... more The optimum designs are given for columns which are elastically clamped at both ends and under concentrated and distributed axial loads. The objective is to maximize the buckling load subject to volume and maximum stress constraints. The results for a minimum area constraint are also obtained for comparison. Under a distributed axial load, the stress constraint leads to different minimum

Procedia Engineering, 2011

ABSTRACT Curved panels are used extensively in several branches of engineering and in particular ... more ABSTRACT Curved panels are used extensively in several branches of engineering and in particular in marine and aerospace engineering working mostly under compressive loads. Failure of these components by buckling or excessive stress is an important design consideration. In the present study the effect of fiber orientation is studied on the failure load of a laminated curved panel subject to uniaxial compression. The failure modes are specified as first-ply failure and buckling with the failure load defined as the minimum of these two loads. The panel is taken as a symmetrically laminated angle-ply plate and the failure load is determined for different aspect ratios, panel thicknesses and boundary conditions (simply supported and clamped panels). The failure load is maximized for a set of selected stacking sequences by determining the best ply angle for each stacking sequence giving the highest failure load.

Thin-Walled Structures, 2011

A curved axisymmetric shell finite element based on a consistent first-order shear deformable she... more A curved axisymmetric shell finite element based on a consistent first-order shear deformable shell theory is developed for the linear stability analysis of cross-ply laminated shells of revolution under compressive loads. Finite element analysis results are presented for isotropic, orthotropic and cross-ply laminated shells of revolution in comparison with the analytical and numerical results found in the literature. These comparisons

Optimal Control Applications and Methods, 2009

ABSTRACT The optimum designs are given for columns, which are simply supported and under distribu... more ABSTRACT The optimum designs are given for columns, which are simply supported and under distributed and concentrated axial loads. The objective is to maximize the buckling load subject to volume and maximum stress constraints. The area of the minimum cross-section under a stress constraint is not known a priori as it depends on the maximum buckling load which in turn depends on the optimum shape. This minimum cross-sectional area is computed as part of an iterative procedure. An iterative solution method is developed based on finite elements and the results are obtained for n=1, 2, 3, defined as I =αnAn with I being the moment of inertia, and A the cross-sectional area. Numerical results show that the optimal areas become larger in the direction of the distributed load. Results are given for uniformly and triangular distributed loads, which are shown to have distinct effects on the optimal column shape. Copyright © 2009 John Wiley & Sons, Ltd.

Journal of Thermoplastic Composite Materials, 2013

In-plane prebuckling stresses arise under axial edge loading as a result of a plate boundary bein... more In-plane prebuckling stresses arise under axial edge loading as a result of a plate boundary being restrained from deformation in the plane of the plate. These stresses exhibit a uniform distribution only under a special set of boundary conditions and in general such uniform in-plane stress distributions do not exist under most boundary conditions encountered in practice. In the present study, in-plane prebuckling stresses are investigated for various in-plane boundary constraints and the stress contour lines are given for rectangular cross-ply laminated plates under linearly varying edge loads. The second part of the article involves the computation of the optimal layer thickness to maximize the buckling load under various combinations of in-plane boundary restraints. The numerical solutions are obtained by finite elements based on first-order shear deformable plate theory which include the in-plane deformations as nodal degrees of freedom. Numerical results show that the exclusion...

Journal of the Franklin Institute, 2007

Two algorithms based on an integral equation formulation of the buckling optimization problem are... more Two algorithms based on an integral equation formulation of the buckling optimization problem are formulated and implemented. The objective of the optimization is to maximize the buckling load of an elastically restrained column by optimally designing the cross-sectional area subject to a minimum cross-section or maximum stress constraint. The first approach involves solving the resulting integral equations iteratively taking into

Journal of Engineering Mechanics, 2013