This work presents a new four-node quadrilateral finite element developed for the linear bending analysis of plate structures. The element is formulated using a strain-based approach consistent with Kirchhoff plate theory and employs three degrees of freedom at each vertex. Its performance is evaluated through a set of standard benchmark tests involving various plate geometries, loading scenarios, and boundary conditions. Numerical results confirm high accuracy, strong resistance to mesh distortion, and rapid convergence, even for relatively coarse meshes. These features indicate that the proposed element offers a reliable and computationally efficient solution for plate analysis in practical engineering problems.

This work presents a new four-node quadrilateral finite element developed for the linear bending analysis of plate structures. The element is formulated using a strain-based approach consistent with Kirchhoff plate theory and employs three degrees of freedom at each vertex. Its performance is evaluated through a set of standard benchmark tests involving various plate geometries, loading scenarios, and boundary conditions. Numerical results confirm high accuracy, strong resistance to mesh distortion, and rapid convergence, even for relatively coarse meshes. These features indicate that the proposed element offers a reliable and computationally efficient solution for plate analysis in practical engineering problems.

This work presents a new four-node quadrilateral finite element developed for the linear bending analysis of plate structures. The element is formulated using a strain-based approach consistent with Kirchhoff plate theory and employs three degrees of freedom at each vertex. Its performance is evaluated through a set of standard benchmark tests involving various plate geometries, loading scenarios, and boundary conditions. Numerical results confirm high accuracy, strong resistance to mesh distortion, and rapid convergence, even for relatively coarse meshes. These features indicate that the proposed element offers a reliable and computationally efficient solution for plate analysis in practical engineering problems.

A comprehensive study of the lithological, sedimentological and palaeontological characteristics of deposits belonging to the middle Turonian to Coniacian age in the Bellezma-Batna Mountains was carried out in order to establish a new biostratigraphic framework and interpret the evolution of the palaeoenvironment and sea-level fluctuation during this period. The studied sequences, exposed at Chaabet (Djebel Boukezzez) and Chihat, are mostly composed of marls and limestones. They are mainly composed of three formations: the Marly Limestone of the Chaabet Formation, the Upper Limestone of the Berriche Formation and the Marls of the Chaabet Formation. Biostratigraphic interpretations were based mainly on planktic and benthic foraminifera (H. helvetica, Marginotruncana cf. sigali, Discorbis turnicus, Nezzazatinella picardi HENSON), ostracods (Ovocytheridea sp., Brachycythere ekpo), and rudists Vaccinites praegiganteus, from the lower limestone member at both the Chaabet and Chihat sections, which is considered as a good indicator of the Upper Turonian age. Fourteen types of microfacies were identified and grouped into three facies assemblages- outer, middle, and inner ramp—based on sedimentological and palaeontological features. Sequence stratigraphic analysis establishes five sedimentary sequences that mark successive cycles of transgression and regression. A significant rise in sea level during the middle Turonian led to deep open marine conditions, followed by a regression in the late Turonian and early Coniacian that led to progressively shallower environments. These fluctuations reflect the combined effects of eustatic changes and regional tectonic movements.

A comprehensive study of the lithological, sedimentological and palaeontological characteristics of deposits belonging to the middle Turonian to Coniacian age in the Bellezma-Batna Mountains was carried out in order to establish a new biostratigraphic framework and interpret the evolution of the palaeoenvironment and sea-level fluctuation during this period. The studied sequences, exposed at Chaabet (Djebel Boukezzez) and Chihat, are mostly composed of marls and limestones. They are mainly composed of three formations: the Marly Limestone of the Chaabet Formation, the Upper Limestone of the Berriche Formation and the Marls of the Chaabet Formation. Biostratigraphic interpretations were based mainly on planktic and benthic foraminifera (H. helvetica, Marginotruncana cf. sigali, Discorbis turnicus, Nezzazatinella picardi HENSON), ostracods (Ovocytheridea sp., Brachycythere ekpo), and rudists Vaccinites praegiganteus, from the lower limestone member at both the Chaabet and Chihat sections, which is considered as a good indicator of the Upper Turonian age. Fourteen types of microfacies were identified and grouped into three facies assemblages- outer, middle, and inner ramp—based on sedimentological and palaeontological features. Sequence stratigraphic analysis establishes five sedimentary sequences that mark successive cycles of transgression and regression. A significant rise in sea level during the middle Turonian led to deep open marine conditions, followed by a regression in the late Turonian and early Coniacian that led to progressively shallower environments. These fluctuations reflect the combined effects of eustatic changes and regional tectonic movements.

A comprehensive study of the lithological, sedimentological and palaeontological characteristics of deposits belonging to the middle Turonian to Coniacian age in the Bellezma-Batna Mountains was carried out in order to establish a new biostratigraphic framework and interpret the evolution of the palaeoenvironment and sea-level fluctuation during this period. The studied sequences, exposed at Chaabet (Djebel Boukezzez) and Chihat, are mostly composed of marls and limestones. They are mainly composed of three formations: the Marly Limestone of the Chaabet Formation, the Upper Limestone of the Berriche Formation and the Marls of the Chaabet Formation. Biostratigraphic interpretations were based mainly on planktic and benthic foraminifera (H. helvetica, Marginotruncana cf. sigali, Discorbis turnicus, Nezzazatinella picardi HENSON), ostracods (Ovocytheridea sp., Brachycythere ekpo), and rudists Vaccinites praegiganteus, from the lower limestone member at both the Chaabet and Chihat sections, which is considered as a good indicator of the Upper Turonian age. Fourteen types of microfacies were identified and grouped into three facies assemblages- outer, middle, and inner ramp—based on sedimentological and palaeontological features. Sequence stratigraphic analysis establishes five sedimentary sequences that mark successive cycles of transgression and regression. A significant rise in sea level during the middle Turonian led to deep open marine conditions, followed by a regression in the late Turonian and early Coniacian that led to progressively shallower environments. These fluctuations reflect the combined effects of eustatic changes and regional tectonic movements.

A comprehensive study of the lithological, sedimentological and palaeontological characteristics of deposits belonging to the middle Turonian to Coniacian age in the Bellezma-Batna Mountains was carried out in order to establish a new biostratigraphic framework and interpret the evolution of the palaeoenvironment and sea-level fluctuation during this period. The studied sequences, exposed at Chaabet (Djebel Boukezzez) and Chihat, are mostly composed of marls and limestones. They are mainly composed of three formations: the Marly Limestone of the Chaabet Formation, the Upper Limestone of the Berriche Formation and the Marls of the Chaabet Formation. Biostratigraphic interpretations were based mainly on planktic and benthic foraminifera (H. helvetica, Marginotruncana cf. sigali, Discorbis turnicus, Nezzazatinella picardi HENSON), ostracods (Ovocytheridea sp., Brachycythere ekpo), and rudists Vaccinites praegiganteus, from the lower limestone member at both the Chaabet and Chihat sections, which is considered as a good indicator of the Upper Turonian age. Fourteen types of microfacies were identified and grouped into three facies assemblages- outer, middle, and inner ramp—based on sedimentological and palaeontological features. Sequence stratigraphic analysis establishes five sedimentary sequences that mark successive cycles of transgression and regression. A significant rise in sea level during the middle Turonian led to deep open marine conditions, followed by a regression in the late Turonian and early Coniacian that led to progressively shallower environments. These fluctuations reflect the combined effects of eustatic changes and regional tectonic movements.

This paper focuses on evaluating the settlement and bearing capacity of compressible soil reinforced with stone columns, by applying load compensation through embankment bodies of varying heights at the level of the column heads and the surrounding soil, the latter is a soil formation consisting of a clay layer containing within it a group of columns embedded in the layer in the form of a square mesh resting in turn on a layer of marl, through a load distribution and transfer mattress located above them spread along the group of columns and the same loads are applied to both models of the unit cell and the isolated column in order to perceive how the three models of distinct geometric shape act and produce an effect on the results of instantaneous settlements obtained for an applied static load. In addition, the bearing capacity for the isolated column model is estimated, based on the theoretical principle of Datye (1982), describing the failure mechanism of a top-loaded isolated stone column embedded in a compressible layer, which was analyzed and developed by Greenwood 1970. Using a calculation code (Flac 3D), numerical simulations were performed to obtain and analyze the settlements for the three models, and the bearing capacity for the isolated column model. The numerical results are estimated using other methods and analytical approaches available in the literature that support this line of research. The comparison of settlement results between the numerical models related to the study of this analysis to indicate that both column group and isolated column models show deviations and quantitative differences correlatively low estimated in percentage between − 5.8% and + 8.8% explaining a suitable and adequate convergence. On the other hand, divergences were recorded are more considerable between the column group model and the composite unit cell ranging from + 64% to + 127%, as well as between the isolated column and the composite cell from + 51% to + 126%. These results highlight that the composite cell systematically reduces settlements, while the group model can be considered as the most significant, especially under high applied loads. Regarding the bearing capacity, some analytical methods present a suitable and almost similar estimation of numerical values with reduced percentages varying between − 1.18% and + 1.34%.

This paper focuses on evaluating the settlement and bearing capacity of compressible soil reinforced with stone columns, by applying load compensation through embankment bodies of varying heights at the level of the column heads and the surrounding soil, the latter is a soil formation consisting of a clay layer containing within it a group of columns embedded in the layer in the form of a square mesh resting in turn on a layer of marl, through a load distribution and transfer mattress located above them spread along the group of columns and the same loads are applied to both models of the unit cell and the isolated column in order to perceive how the three models of distinct geometric shape act and produce an effect on the results of instantaneous settlements obtained for an applied static load. In addition, the bearing capacity for the isolated column model is estimated, based on the theoretical principle of Datye (1982), describing the failure mechanism of a top-loaded isolated stone column embedded in a compressible layer, which was analyzed and developed by Greenwood 1970. Using a calculation code (Flac 3D), numerical simulations were performed to obtain and analyze the settlements for the three models, and the bearing capacity for the isolated column model. The numerical results are estimated using other methods and analytical approaches available in the literature that support this line of research. The comparison of settlement results between the numerical models related to the study of this analysis to indicate that both column group and isolated column models show deviations and quantitative differences correlatively low estimated in percentage between − 5.8% and + 8.8% explaining a suitable and adequate convergence. On the other hand, divergences were recorded are more considerable between the column group model and the composite unit cell ranging from + 64% to + 127%, as well as between the isolated column and the composite cell from + 51% to + 126%. These results highlight that the composite cell systematically reduces settlements, while the group model can be considered as the most significant, especially under high applied loads. Regarding the bearing capacity, some analytical methods present a suitable and almost similar estimation of numerical values with reduced percentages varying between − 1.18% and + 1.34%.

This paper focuses on evaluating the settlement and bearing capacity of compressible soil reinforced with stone columns, by applying load compensation through embankment bodies of varying heights at the level of the column heads and the surrounding soil, the latter is a soil formation consisting of a clay layer containing within it a group of columns embedded in the layer in the form of a square mesh resting in turn on a layer of marl, through a load distribution and transfer mattress located above them spread along the group of columns and the same loads are applied to both models of the unit cell and the isolated column in order to perceive how the three models of distinct geometric shape act and produce an effect on the results of instantaneous settlements obtained for an applied static load. In addition, the bearing capacity for the isolated column model is estimated, based on the theoretical principle of Datye (1982), describing the failure mechanism of a top-loaded isolated stone column embedded in a compressible layer, which was analyzed and developed by Greenwood 1970. Using a calculation code (Flac 3D), numerical simulations were performed to obtain and analyze the settlements for the three models, and the bearing capacity for the isolated column model. The numerical results are estimated using other methods and analytical approaches available in the literature that support this line of research. The comparison of settlement results between the numerical models related to the study of this analysis to indicate that both column group and isolated column models show deviations and quantitative differences correlatively low estimated in percentage between − 5.8% and + 8.8% explaining a suitable and adequate convergence. On the other hand, divergences were recorded are more considerable between the column group model and the composite unit cell ranging from + 64% to + 127%, as well as between the isolated column and the composite cell from + 51% to + 126%. These results highlight that the composite cell systematically reduces settlements, while the group model can be considered as the most significant, especially under high applied loads. Regarding the bearing capacity, some analytical methods present a suitable and almost similar estimation of numerical values with reduced percentages varying between − 1.18% and + 1.34%.

The development of a mixed carbonate–siliciclastic ramp system along the southern Tethyan margin can be clarified by examining the Aptian–Albian sequence of the Aurès Basin. An extensive cross-section was analysed to constrain the lithological architecture and microfacies distribution along the southern flank of Djebel El Azereg, the most prominent anticline of the area. Lithostratigraphic analysis allows the subdivision of the Aptian–Albian succession into three well-defined units: the Ich Moul Formation, the Dechera Baida Formation, and the Ackliath Azougar Formation. The studied succession is composed of laterally and vertically heterogeneous siliciclastic–carbonate deposits, reflecting the interplay between carbonate productivity and episodic terrigenous input under varying accommodation conditions. Petrographic analysis reveals a diverse suite of microfacies, characterised by significant variations in texture and in the relative abundance of skeletal and non-skeletal components. Thirteen microfacies are distinguished and organised into five facies associations, (1) siliciclastic microfacies, constituted by fine- to medium-grained sandstones; (2) siliciclastic–carbonate microfacies with packstone texture, composed mainly of quartz grains, ooids, bivalves, and orbitolinids; (3 and 4) carbonate microfacies with packstone and/or grainstone texture, dominated by ooids and peloids; and (4) wackestone to packstone microfacies, dominated by bivalves and echinoderms. These facies associations record depositional environments along a low-gradient homoclinal ramp, ranging from coastal and hybrid backshoal settings to carbonate shoals (inner and mid-ramp) and a proximal outer ramp domain. The spatial and vertical distribution of these facies associations provides insights into the internal organisation of the ramp (inner, middle and outer) and its stratigraphic evolution. These results highlight the complex dynamics of mixed carbonate–siliciclastic systems and contribute to a better understanding of Aptian–Albian platform development along the southern Tethyan margin.

The development of a mixed carbonate–siliciclastic ramp system along the southern Tethyan margin can be clarified by examining the Aptian–Albian sequence of the Aurès Basin. An extensive cross-section was analysed to constrain the lithological architecture and microfacies distribution along the southern flank of Djebel El Azereg, the most prominent anticline of the area. Lithostratigraphic analysis allows the subdivision of the Aptian–Albian succession into three well-defined units: the Ich Moul Formation, the Dechera Baida Formation, and the Ackliath Azougar Formation. The studied succession is composed of laterally and vertically heterogeneous siliciclastic–carbonate deposits, reflecting the interplay between carbonate productivity and episodic terrigenous input under varying accommodation conditions. Petrographic analysis reveals a diverse suite of microfacies, characterised by significant variations in texture and in the relative abundance of skeletal and non-skeletal components. Thirteen microfacies are distinguished and organised into five facies associations, (1) siliciclastic microfacies, constituted by fine- to medium-grained sandstones; (2) siliciclastic–carbonate microfacies with packstone texture, composed mainly of quartz grains, ooids, bivalves, and orbitolinids; (3 and 4) carbonate microfacies with packstone and/or grainstone texture, dominated by ooids and peloids; and (4) wackestone to packstone microfacies, dominated by bivalves and echinoderms. These facies associations record depositional environments along a low-gradient homoclinal ramp, ranging from coastal and hybrid backshoal settings to carbonate shoals (inner and mid-ramp) and a proximal outer ramp domain. The spatial and vertical distribution of these facies associations provides insights into the internal organisation of the ramp (inner, middle and outer) and its stratigraphic evolution. These results highlight the complex dynamics of mixed carbonate–siliciclastic systems and contribute to a better understanding of Aptian–Albian platform development along the southern Tethyan margin.

This study presents the development of a enhancedrectangular membrane finite element using the strain-based approach, designed for both elasticand elastoplasticanalyses. Each of the four corner nodes of the element is characterized by three degrees of freedom: two translational degrees and one in-plane rotational degree.The displacement functions of the proposed element accurately capture the rigid body motion modes.For the elastoplastic computations, the material response is evaluated using the Von Mises failure creterion, andthe nonlinear solution procedure incorporates viscoplastic-strain approaches. For validation purposes, several selected numerical examples are solved using the developed element in both linear and nonlinearanalyses.The results obtained are compared with analytical solutions and other similar membrane finite elements, demonstrating the strong performance of the proposed element.

This study presents the development of a enhancedrectangular membrane finite element using the strain-based approach, designed for both elasticand elastoplasticanalyses. Each of the four corner nodes of the element is characterized by three degrees of freedom: two translational degrees and one in-plane rotational degree.The displacement functions of the proposed element accurately capture the rigid body motion modes.For the elastoplastic computations, the material response is evaluated using the Von Mises failure creterion, andthe nonlinear solution procedure incorporates viscoplastic-strain approaches. For validation purposes, several selected numerical examples are solved using the developed element in both linear and nonlinearanalyses.The results obtained are compared with analytical solutions and other similar membrane finite elements, demonstrating the strong performance of the proposed element.

This study presents the development of a enhancedrectangular membrane finite element using the strain-based approach, designed for both elasticand elastoplasticanalyses. Each of the four corner nodes of the element is characterized by three degrees of freedom: two translational degrees and one in-plane rotational degree.The displacement functions of the proposed element accurately capture the rigid body motion modes.For the elastoplastic computations, the material response is evaluated using the Von Mises failure creterion, andthe nonlinear solution procedure incorporates viscoplastic-strain approaches. For validation purposes, several selected numerical examples are solved using the developed element in both linear and nonlinearanalyses.The results obtained are compared with analytical solutions and other similar membrane finite elements, demonstrating the strong performance of the proposed element.

This work presents a novel strain-based finite element formulation specifically designed for the comprehensive analysis of two-dimensional structures under static and dynamic elastoplastic conditions. The proposed triangular element features three degrees of freedom per node, including two in-plane translational components and one rotational component about the normal axis.The displacement field is derived from predefined strain functions that satisfy the compatibility equations, while the interpolation functions are carefully constructed to provide an exact representation of rigid body motions. The developed formulation is applicable to both static and time-dependent elastoplastic analyses.In the static case, the element accurately determines nodal forces, displacements, and stress distributions. For dynamic analyses, a lumped mass matrix combined with an explicit time integration scheme is adopted to improve computational efficiency.The accuracy and robustness of the proposed element are validated through several benchmark test problems, demonstrating its excellent numerical performance and reliability in structural analysis.

This work presents a novel strain-based finite element formulation specifically designed for the comprehensive analysis of two-dimensional structures under static and dynamic elastoplastic conditions. The proposed triangular element features three degrees of freedom per node, including two in-plane translational components and one rotational component about the normal axis.The displacement field is derived from predefined strain functions that satisfy the compatibility equations, while the interpolation functions are carefully constructed to provide an exact representation of rigid body motions. The developed formulation is applicable to both static and time-dependent elastoplastic analyses.In the static case, the element accurately determines nodal forces, displacements, and stress distributions. For dynamic analyses, a lumped mass matrix combined with an explicit time integration scheme is adopted to improve computational efficiency.The accuracy and robustness of the proposed element are validated through several benchmark test problems, demonstrating its excellent numerical performance and reliability in structural analysis.

This work presents a novel strain-based finite element formulation specifically designed for the comprehensive analysis of two-dimensional structures under static and dynamic elastoplastic conditions. The proposed triangular element features three degrees of freedom per node, including two in-plane translational components and one rotational component about the normal axis.The displacement field is derived from predefined strain functions that satisfy the compatibility equations, while the interpolation functions are carefully constructed to provide an exact representation of rigid body motions. The developed formulation is applicable to both static and time-dependent elastoplastic analyses.In the static case, the element accurately determines nodal forces, displacements, and stress distributions. For dynamic analyses, a lumped mass matrix combined with an explicit time integration scheme is adopted to improve computational efficiency.The accuracy and robustness of the proposed element are validated through several benchmark test problems, demonstrating its excellent numerical performance and reliability in structural analysis.

This study presents a reliability-based design optimization (RBDO) framework for improving the intrinsic stability of total hip arthroplasty through jump-distance-based design selection. The problem was formulated using four design variables: femoral head diameter, cup abduction angle, cup anteversion angle, and femoral offset. Jump distance (JD) was computed from an analytical geometric model, and uncertainty was propagated by Monte Carlo simulation with 10,000 samples per scenario. A total of 1,617 configurations were evaluated in MATLAB R2020b using parallel computing. The results showed a mean reliability index of 2.3945, with values ranging from -2.9677 to 3.8906, and a mean Monte Carlo jump distance of 12.0659 mm. The best-performing configuration within the explored design space was a 36 mm head, 30° abduction, 30° anteversion, and -2 mm offset, yielding a nominal JD of 20.601 mm, a mean simulated JD of 20.568 mm, and zero failures in 10,000 trials. Parametric analysis showed that abduction angle had the strongest negative influence on reliability, followed by femoral offset, whereas head diameter had a positive effect and anteversion had a weaker but favorable contribution. These results confirm that a probabilistic design framework can discriminate robust from fragile implant configurations more effectively than a purely deterministic threshold check and provide a computationally efficient basis for preclinical implant-orientation optimization.

This study presents a reliability-based design optimization (RBDO) framework for improving the intrinsic stability of total hip arthroplasty through jump-distance-based design selection. The problem was formulated using four design variables: femoral head diameter, cup abduction angle, cup anteversion angle, and femoral offset. Jump distance (JD) was computed from an analytical geometric model, and uncertainty was propagated by Monte Carlo simulation with 10,000 samples per scenario. A total of 1,617 configurations were evaluated in MATLAB R2020b using parallel computing. The results showed a mean reliability index of 2.3945, with values ranging from -2.9677 to 3.8906, and a mean Monte Carlo jump distance of 12.0659 mm. The best-performing configuration within the explored design space was a 36 mm head, 30° abduction, 30° anteversion, and -2 mm offset, yielding a nominal JD of 20.601 mm, a mean simulated JD of 20.568 mm, and zero failures in 10,000 trials. Parametric analysis showed that abduction angle had the strongest negative influence on reliability, followed by femoral offset, whereas head diameter had a positive effect and anteversion had a weaker but favorable contribution. These results confirm that a probabilistic design framework can discriminate robust from fragile implant configurations more effectively than a purely deterministic threshold check and provide a computationally efficient basis for preclinical implant-orientation optimization.