Base force element method of complementary energy principle for large rotation problems

Using the concept of the base forces, a new finite element method （base force element method, BFEM） based on the complementary energy principle is presented for accurate modeling of structures with large displacements and large rotations. First, the complementary energy of an element is described by taking the base forces as state variables, and is then separated into deformation and rotation parts for the case of large deformation. Second, the control equations of the BFEM based on the complementary energy principle are derived using the Lagrange multiplier method. Nonlinear procedure of the BFEM is then developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the BFEM.

Carbon efficiency evaluation method for urban energy system with multiple energy complementary

Urban energy systems(UESs)play a pivotal role in the consumption of clean energy and the promotion of energy cascade utilization.In the context of the construction and operation strategy of UESs with multiple complementary energy resources,a comprehensive assessment of the energy efficiency is of paramount importance.First,a multi-dimensional evaluation system with four primary indexes of energy utilization,environmental protection,system operation,and economic efficiency and 21 secondary indexes is constructed to comprehensively portray the UES.Considering that the evaluation system may contain a large number of indexes and that there is overlapping information among them,an energy efficiency evaluation method based on data processing,dimensionality reduction,integration of combined weights,and gray correlation analysis is proposed.This method can effectively reduce the number of calculations and improve the accuracy of energy efficiency assessments.Third,a demonstration project for a UES in China is presented.The energy efficiency of each scenario is assessed using six operational scenarios.The results show that Scenario 5,in which parks operate independently and investors build shared energy-storage equipment,has the best results and is best suited for green and low-carbon development.The results of the comparative assessment methods show that the proposed method provides a good energy efficiency assessment.This study provides a reference for the optimal planning,construction,and operation of UESs with multiple energy sources.

Stability and reinforcement analyses of high arch dams by considering deformation effects

The strict definition and logical description of the concept of structure stability and failure are presented. The criterion of structure stability is developed based on plastic complementary energy and its variation. It is presented that the principle of minimum plastic complementary energy is the combination of structure equilibrium, coordination condition of deformation and constitutive relationship. Based on the above arguments, the deformation reinforcement theory is developed. The structure global stability can be described by the relationship between the global degree of safety of structure and the plastic complementary energy. Correspondingly, the new idea is used in the evaluations of global stability, anchorage force of dam-toe, fracture of dam-heel and treatment of faults of high arch dams in China. The results show that the deformation reinforcement theory provides a uniform and practical theoretical framework and a valuable solution for the analysis of global stability, dam-heel cracking, dam-toe anchorage and reinforcement of faults of high arch dams and their foundations.

Nonlinear stability of double-deck reticulated circular shallow spherical shell

Based on the variational equation of the nonlinear bending theory of doubledeck reticulated shallow shells, equations of large deflection and boundary conditions for a double-deck reticulated circular shallow spherical shell under a uniformly distributed pressure are derived by using coordinate transformation means and the principle of stationary complementary energy. The characteristic relationship and critical buckling pressure for the shell with two types of boundary conditions are obtained by taking the modified iteration method. Effects of geometrical parameters on the buckling behavior are also discussed.

Two-dimensional parasitic capacitance extraction for integrated circuit with dual discrete geometric methods

Capacitance extraction is one of the key issues in integrated circuits and also a typical electrostatic prob- lem. The dual discrete geometric method （DGM） is investigated to provide relative solutions in two-dimensional unstructured mesh space. The energy complementary characteristic and quick field energy computation thereof based on it are emphasized. Contrastive analysis between the dual finite element methods and the dual DGMs are presented both from theoretical derivation and through case studies. The DGM, taking the scalar potential as unknown on dual interlocked meshes, with simple form and good accuracy, is expected to be one of the mainstreaming methods in associated areas.