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THE idea of a dual analysis in finite elements of a given structure was put forward in Ref. 4. The first analysis should be of the displacement type, using conforming displacement models of the finite elements. This results in a continuous, piecewise differcntiable displacement field in the whole structure, for which linear elasticity theory predicts lower bounds to the local static influence coefficients. The second analysis should be based on equilibrium models of the finite elements. The stress field within the structure is then continuously transmitted across the interfaces and satisfies detailed equilibrium conditions in the interior of each element. This property furnishes upper bounds to the influence coefficients.

We describe how to improve the accuracy of stress in the application of the hybrid finite element method. The idea is based on the fact that the assumed stress hybrid method is equivalent to both the principle of minimum complementary energy within the interior of each element and the principle of the minimum potential energy in the entire domain. It is known that when a good hybrid model is used for the displacement solution, the stress model must satisfy equilibrium within individual elements and be comparable with the boundary displacements. However, the compatibility in the elements is usually ignored and through variational operation it may be only approximately satisfied. So the stress model cannot approach a corresponding analytical stress field. In the present study, after nodal displacements are solved, we propose that a different stress model could be used to find the stress coefficients according to the principle of minimum complementary energy in each element in order to get an improved stress field.

Based on the recent advances of hybrid stress finite elements, a series of alternative stress assumptions for these elements are investigated. Several new element models are proposed by using different concepts for the stress interpolation. Under a unified formulation presented in this paper for Hellinger—Reissner principle based hybrid stress element models, the element series 5β‐family for plane stress and 18β‐family for three‐dimensional problems are discussed. The extra incompatible displacements sometimes also added are not introduced in this unified formulation. A number of popular benchmark elastic problems are examined for both two element families. In each family, the element model presented in this paper using normalized transformed higher order stress trials usually gives better predictions than the others.

The purpose of this paper is to acquire strict upper and lower bounds on quantities of slender beams on Winkler foundation in finite element analysis.

It leans on the dual analysis wherein the constitutive relation error (CRE) is used to perform goal-oriented error estimation. Due to the coupling of the displacement field and the stress field in the equilibrium equations of the beam, the prolongation condition for the stress field which is the key ingredient of CRE estimation is not directly applicable. To circumvent this difficulty, an approximate problem and the solution thereof are introduced, enabling the CRE estimation to proceed. It is shown that the strict bounding property for CRE estimation is preserved and strict bounds of quantities of the beam are obtainable thereafter.

Numerical examples are presented to validate the strict upper and lower bounds for quantities of beams on elastic foundation by dual analysis.

This paper deals with one-dimensional (1D) beams on Winkler foundation. Nevertheless, the present work can be naturally extended to analysis of shells and 2D and 3D reaction-diffusion problems for future research.

CRE estimation is extended to analysis of beams on elastic foundation by a decoupling strategy; strict upper bounds of global energy norm error for beams on elastic foundation are obtained; strict bounds of quantities for beams on elastic foundation are also obtained; unified representation and corresponding dual analysis of various quantities of the beam are presented; rigorous derivation of admissible stresses for beams is given.

A new laminated composite plate finite element is proposed that is numerically stable and accurate in displacements and stresses, including transverse shear stress. The formulation is based on the Hellinger—Reissner principle with Mindlin kinematics. All stress components are given independent approximations and do not satisfy equilibrium conditions a priori. A novel feature of the formulation is the additive decomposition of the displacement field into two parts corresponding to nodal interpolations and independent local basis functions. The additional basis functions and their associated parameters play an important role in characterizing the accuracy of the element. These functions eliminate shear locking in the lower order elements and provide additional variational constraints on the stresses, leading to very accurate results. A 4‐node and a 9‐node version are developed and it is shown that both elements pass the patch test suggested by Zienkiewicz et al. and are stable in the sense of the Babuška—Brezzi condition. The special structure of the element flexibility matrix provides computational efficiency approaching that of displacement based formulations.

The purpose of this paper is to test hypotheses about the effects of economic and weather factors on the inventories of cattle, sheep and goats in Inner Mongolia Autonomous Region (IMAR).

An equilibrium displacement model of livestock products is combined with an inventory relation proposed by Rucker et al. (1984) to deduce hypothesis about the effects of expected price and feed costs, weather, and supply and demand shifters on herd size. Dynamics are incorporated using the partial adjustment and adaptive expectations models originally proposed by Nerlove (1956). The hypotheses are tested using both the structural equations implied by the model, and the reduced form.

Results suggest livestock inventories in IMAR in general are more responsive to weather conditions than to economic conditions. This is especially true for cattle and sheep, where isolated 1 percent changes in weather variables, namely precipitation and radiation, were found to have a much larger effect on inventory than isolated 1 percent changes in expected price and forage costs. The effects of the weather variables, moreover, were found to be different for goats than for cattle and sheep, with goat numbers decreasing with improvements in weather, and cattle and sheep numbers increasing. This suggests herders respond to poor weather in part by substituting goats for cattle and/or sheep. Price was found to have a negative effect on cattle inventory, and no effect on sheep and goat inventory. Forage costs were found to have a positive effect on cattle and sheep inventories, and no effect on goat inventory. These results suggest policies to protect grassland by controlling inventory levels must be designed carefully if they are to be effective.

The paper makes a methodological contribution in that the livestock inventory relation proposed by Rucker et al. (1984) is extended to include supply and demand shifters for livestock products in a partial-equilibrium setting where the industry in question is a net exporter of livestock products. The paper makes an empirical contribution in that additional evidence is provided on the role that price plays in inventory behavior.

The purpose of this paper is to present a two-dimensional (2D) model of the base force element method (BFEM) based on the complementary energy principle. The study proposes a model of the BFEM for arbitrary mesh problems.

The BFEM uses the base forces given by Gao (2003) as fundamental variables to describe the stress state of an elastic system. An explicit expression of element compliance matrix is derived using the concept of base forces. The detailed formulations of governing equations for the BFEM are given using the Lagrange multiplier method. The explicit displacement expression of nodes is given. To verify the 2D model, a program on the BFEM using MATLAB language is made and a number of examples on arbitrary polygonal meshes and aberrant meshes are provided to illustrate the BFEM.

A good agreement is obtained between the numerical and theoretical results. Based on the studies, it is found that the 2D formulation of BFEM with complementary energy principle provides reliable predictions for arbitrary mesh problems.

Due to the use of Lagrange multiplier method, there are more basic unknowns in the control equation. The proposed method will be improved in the future.

This paper presents a new idea and a new numerical method, and to explore new ways to solve the problem of arbitrary meshes.

The paper presents a 2D model of the BFEM using the complementary energy principle for arbitrary mesh problems.

The purpose of this paper is to develop an equilibrium displacement model (EDM) that is able to evaluate the impacts of a free trade agreement (FTA) on the profits of farmers. Empirical applications of the developed EDM are performed for evaluating the influences of Korea-Chile FTA on the grape industry in Korea.

Supply and demand equations together with profit function of individual farmers are converted into log-differential forms that compose the EDM. The cost function of grape producers is estimated for deriving the parameters that are required in applying the developed EDM.

The share of profit within revenue and the elasticity of cost with respect to quantity in the cost function play key roles in assessing the change in farmers’ profit. The empirical assessment of the effects of Korea-Chile FTA indicates that this FTA has little impact on the Korean grape market and grape producers in Korea.

Usefulness of the existing EDM has been limited in evaluating the impacts of exogenous shocks on the individual farmer level. This paper fills this gap by developing an EDM that assesses the impacts of tariff reduction on farm-level profit.

Since 2004, subsidies increased by 670 percent in the Chinese fertilizer industry to reduce the farmer's burden. The purpose of this paper is to assess whether subsidies benefit the target groups, the fertilizer subsidy distribution pattern and benefit allocation pattern among fertilizer producers and other sectors were investigated.

The Muth model is extended to evaluate the impacts of a subsidy on multi-stage markets.

It is found that the total benefits from the policy are about RMB 7.7 billion yuans. The fertilizer suppliers gain about RMB 51 billion yuans from the favorable policy with mean subsidy incidence 0.8 and capturing about 70 percent of total surplus.

The results suggest that transferring parts of subsidies to the non-fertilizer sectors could be considered an efficient way to redistribute welfare indifferent sectors.

This study first use the equilibrium displacement model to quantity the distribution of fertilizer subsidy in a vertical market in China.

The purpose of this paper is to investigate the implications of the China’s rising meat demand and industrialization of the livestock sector for the vegetable oil market.

An equilibrium displacement model is constructed to analyze the interactions between meat consumption and vegetable oil market through the development of livestock sector modernization. Parameters derived from the 2006 to 2009 data are first used to produce the counterfactual growth rate of the non-soybean vegetable oil to validate the model. Then the authors use the second set of parameters derived from the 2010 to 2013 data to forecast the changes in the vegetable oil market in China.

Soybean oil, as a co-product of soybean processing, tends to crowd out other vegetable oils. In particular, the authors find that the market for non-soybean vegetable oils may shrink as long as the rapid industrialization pace above 10 percent within China’s livestock sector continues. Although their production takes up only 8.5 percent of all agricultural lands in China, oil crops remain as important cash crops for farmers contributing over 10 percent to the overall farm income in some provinces. The authors’ analysis suggests that stakeholders in these regions should closely monitor the structural changes within the livestock sector and consider the information for crop selection.

The authors’ analysis contributes to the literature on China’s meat demand by highlighting its implications for other agricultural markets involved in the food system.