Water supply networks account for a major portion of the urban infrastructure requiring sizable funds for their construction and operation. This has encouraged many researchers to focus their efforts on optimizing water distribution networks. In most recent research in the field، stochastic meta-heuristic algorithms have been employed to address the problem. Given the many inadequacies of stochastic algorithms، the present study explored the application of a novel deterministic algorithm for minimizing pipe-sizing costs in water distribution systems (WDS). METHODs: The algorithm used in this study is a modified version of the central FORCE optimization algorithm called CFONet which is used for solving water distribution system problems. The performance of the proposed METHOD was evaluated by optimizing pipe-sizing in two benchmark WDSs. For this purpose، both CFO and CFONet METHODs were written in MATLAB and interfaced with the hydraulic simulation model EPANET. Results and discussion: Application of the two METHODs mentioned above to two different water supply systems revealed the superior performance of the proposed CFOnet over its CFO counterpart. Thus، CFOnet yielded an optimum response for the deisgn of a double ringed system equal to US$419، 000 after 12، 432 runs of objective function estimations. Moreover، the optimum design of a CAdo system was obtained to cost 126، 535، 915 In. Ruppes after 259، 476 runs of objective function estimations. Conclusion: Comparison of the results obtained in this study with those reported in the literature on other stochastic optimization algorithms showed that the proposed METHOD yields satisfactory solutions for WDSs optimization problems while it also enjoys the merits of a deterministic optimization METHOD.

Graph theoretical FORCE METHODs are highly efficient for the generation of sparse and banded null bases and flexibility matrices, however, these METHODs require special considerations when the support conditions are indeterminate. These considerations with special METHODs are presented in this paper which leads to efficient utilization of graph theoretical FORCE METHOD for indeterminate support conditions with no substantial decrease in sparsity.

Headgear provides an extra-oral anchorage and is needed in many treatment procedures. Application of a headgear needs a complete knowledge of the involved active and reactive FORCEs. The main goal of this study was to make clear the very events of a cervical headgear use. The finite element METHOD of analysis was chosen to accomplish the research. A 3D F.E.M. model consisting of a cervical headgear and two separate blocks as the terminal molars were designed and a 200 grf. Was applied at each side and the results were obtained. The most important result was the consideration of the elastic deformation of the outer bow and its effect on the FORCE delivered to the terminal molar. A brief discussion of the differences between the manual calculation of the FORCEs and the results obtained by the F.E.M. was presented at the end of the article.

Formation of a suitable null basis is the main problem of finite elements analysis via FORCE METHOD. For an optimal analysis, the selected null basis matrices should be sparse and banded corresponding to sparse, banded and well-conditioned flexibility matrices. In this paper, an efficient METHOD is developed for the formation of the null bases of finite element models (FEMs) consisting of tetrahedron elements, corresponding to highly sparse and banded flexibility matrices. This is achieved by associating special graphs with the FEM and selecting appropriate sub graphs and forming the self-equilibrating systems (SESs) on these sub graphs. Two examples are presented to illustrate the simplicity and effectiveness of the presented graph algebraic METHOD.

Different METHODs are used for the formation of the null basis matrix of a structure followed by calculating the element FORCEs when the FORCE METHOD of structural analysis is utilized. Singular value decomposition (SVD) METHOD is one of the algebraic METHODs in FORCE METHOD that uses equilibrium matrix in its computation of finding element FORCEs. By increasing the dimensions of the equilibrium matrix in large scale structures, the time needed for making orthogonal matrices grows. In recent decades many researchers have worked on block-diagonalization of structural matrices such as stiffness matrix in symmetric structures to reduce the computational time and simplify the equations. Block-diagonalization of equilibrium matrix can also reduce the computational time in algebraic FORCE METHODs. In this paper block-diagonalization of equilibrium matrices of circulant structure is performed using Kronocker product and SVD METHOD is utilized to calculate the block-diagonalization null basis matrix. Finally the results are compared to those of the METHOD without block-diagonalization and other algebraic METHODs.

This paper presents a FORCE (flexibility) based formulation for nonlinear static analysis of reinFORCEd concrete plane frames. Nonlinear behavior of concrete and steel fibers based on a simple one-dimensional constitutive law is considered. Navier- Bernoulli theory is accepted in different sections and the effect of bond-slip is, thus, neglected. The section flexibility and stiffness matrices are extracted by direct integration of tangential modulus of materials all over the sections. Flexibility, stiffness and residual FORCE vector of elements are estimated, using principle of virtual work and based on a FORCE (flexibility) formulation. An iterative algorithm used to satisfy the proposed convergence criterion. Presented samples show accuracy and efficiency of the proposed METHOD in contrast to other existing numerical and experimental results.    

In this paper an efficient METHOD is developed for the formation of null bases of finite element models (FEMs) composed of rectangular and triangular plane stress and plane strain elements, corresponding to highly sparse and banded flexibility matrices. This is achieved by associating special graphs to the finite element models and selecting appropriate subgraphs for the formation of localized self stress systems. The efficiency of the present METHOD is illustrated through some examples.

In this paper, performance-based seismic design METHOD for eccentrically braced frames is implemented. This METHOD combines the advantages of the FORCE based, and the displacement based design METHODs "so called" hybrid FORCE-displacement design METHOD (HFD). The applied METHOD transforms the maximum inter-story drift and local ductility into target roof displacement and then for ductility and strength reduction factor, proposes several formulas. For this purpose, sixty eccentrically braced steel frames with different number of: stories, bay widths, number of spans, various bracing dimensions, etc. were analyzed using nonlinear static analysis METHOD (Push Over Analysis). Then, nonlinear multiple-parameter regression model was utilized for proposing the formulas for the strength reduction factor and ductility. Lateral loading system type, earthquake level, slenderness of braces, intensity of earthquake, number of roofs and bays were influenced the obtained formulas. The obtained results in compare with FORCE based, and direct displacement based METHODs show that the seismic responses such as roof displacement and base shear have reliable accuracies. Furthermore, the results indicate that in compare with FORCE-based and displacement based design METHODs, the members of designed frames using the hybrid METHOD are economical.